The plane is such a mess of chaos and upheaval that it doesn't even stay the same in basic state from time to time, which is another way of saying the writers can't keep it straight and change it whenever it's convenient. It's an infinite plane, like the others, but actually has an infinite number of different layers as well, meaning that the aforementioned changes might just be an examination of a different subset of layers. According to one faction in the Planescape setting it also specifically has 666 layers, because that's totally the same as infinite. Then again, it's one of the chaotic planes, so not making sense is probably the whole idea.
Most of the layers are often described as containing wildly different inhospitable biomes, sometimes on the same layer side-by-side. All of them are full of the kind of Chaoticy-Evilly fuckery you'd expect, so none of them are great places for vacation homes. The named layers are also given numbers, but given that they are in no way consistently arranged in space, those numbers are meaningless and changed often. Officially, though, they are numbered in order of their discovery by mortals.
Pazunia: 1st Layer
The Plane of Infinite Portals, and the way you get to any of the others. It's covered in giant sinkholes, each one a portal to another layer of the Abyss. This is also the layer that the River Styx flows through on its path from Pandemonium to Acheron. Iron fortresses on this layer are also where Demon Princes leave their bodies when they're busy roaming around the Astral Plane. Dozens of minor demon princes co-rule this layer, though, officially, Pazuzu is in charge. The Grand Abyss is sometimes the 4th layer and Pazunia is the Styx shorelines.
This is one of the great battlefields of the Blood War. Mostly, this is a staging ground for the various demon hordes being flung at the Nine Hells, but that creates a whole set of problems by itself. As some of you may already know, beings that are inherent Chaotic and Evil are just as likely to start axe-murdering one another as anything else. So put a million such beings of pure Chaotic Evil side by side in one place, and count the seconds until they just start killing each other instead of doing what they were told. Now, complicate that problem with the fact that some demon princes may actually want such an outburst to occur to weaken the forces of a rival. Now throw in yugoloth mercenaries turning stag on a demon employer (devils, after all, are much better at keeping their words on contracts and payments and the like). Toss in a force of devils being sent for scouting and/or raiding duties to better prepare for said horde before it even gets to Avernus. And finally, sprinkle in the dozens of other planars - celestials, adventurers, etc. - who are visiting and know that the best way to deal with an ornery demon is basically to fucking destroy it.
Now, it's not all murderhobos and axes to the face. There's a few fiends that run some odd little fortified establishments out here. Some are mercenaries who can press-gang enough demons to make it worth someone's effort to pay for it. There's even a few mercantile or entertainment venues around. But mostly, if you run into a fiend out here, you murder the shit out of it and hope it didn't have any friends who really gave a shit about it. This is the first layer of an infinite amount of Chaotic Evil, by the way; it only gets more fun the further down the spiral you go.
It should be noted that oddly, this is the most stable layer of the Abyss. No, really: it hasn't actually changed all that much, fundamentally, in all of existence. The demons that inhabit it, and who's running what, that does change, and yes, the land itself has been ripped up, rebuilt, wash, rinse, repeat. But this is basically where the teeming, seething primordial chaos of the Abyss touches reality, and thus this connection is by necessity stable. (Since if the Abyss disconnected, even temporarily, it would probably be adrift in the Astral, or possibly it would fuck off from reality altogether for the Far Realm; it's hard to say what the metaphysics of that scenario would look like.)
Driller's Hives: 2nd Layer
This horrible place is one of the most unpleasantly inhospitable layers in all of the Abyss. It's not so much because of the indigenous fiendish insects who try to kill anything on sight, but because of how all visitors who enter risk contracting a horrible disease that causes the sufferer to break out in hatching insect eggs until the afflicted dies and decomposes into a mass of rot and insect eggs over the course of minutes. The addition of the giant, intelligent fiendish insect thralls of the ruler, Tharzax the Chattering Prince, help make the whole place a big, sentient shit-sprinkle-covered crapcake of NOPE.
The Forgotten Land: 3rd Layer
This is an almost endless landscape of empty ruins that suggest a once bustling city. No demons, other than the layer's Lord, Zzyczesiya The Ungrasped, master of malevolent ignorance and confusion, come here. The place was abandoned due to a catastrophe, for which Zzyczesiya has been traditionally blamed, and now, entering the layer causes any sentient being's mind, even those of demons and sapient undead, to fritter away like moist cotton candy, leaving visitors as catatonic and braindead. Constructs are immune to the effects, and persistent visitors often use golem stand-ins to explore this godawful place. Allegedly, Zzyczesiya destroyed all the original inhabitants by accident, 1st through 3rd edition claiming by changing the course of the River Styx, and was punished by imprisonment in the Wells of Darkness. Zzyczesiya would escape, and return to the Forgotten Land in order to use the power of this layer to unremember something really, really, really horrible (possibly a first draft of the script for Gigli).
The Grand Abyss: 4th Layer
What starts as a gaping chasm on the first layer is an infinitely deep pit where the walls are dotted with portals which connect to all of the other layers in the plane. Navigation is tricky because the only dimensions of relevance are vertical, so you need to either fly or be a patient climber. This place was created by the now-dead Lord, Asima The Unanticipated, who apparently died because she(?) didn't anticipate pissing off the Queen of Chaos enough to assassinate her. Now, Asima's corpse lies in her tomb, the Tumulus of Abhorrence, which is filled with treasure and secrets, and is guarded by her "seraph," a super-demon named "Guardian of the Gates" who pretty much super-kills anyone unlucky enough to encounter him. Guardian of the Gates periodically leaves his master's tomb to harass/super-kill schmucks in the Grand Abyss, as per his master's original orders: adventurers stupid enough to think that there are no other defenders of the Tumulus tend to die screaming.
Realm of a Million Eyes: 6th layer
Home of the Great Mother, princess of the Beholders. Presumably not a great place to be for anyone else, because no one's ever bothered to describe it in detail.
Phantom Plane: 7th layer
Ruled by Sess'lnnek the other god of the lizardfolk. He grew bored with the Tanar'ri's Blood War, withdrew and officially closed the layer off so that no one can enter without his explicit permission.
Skin-shedder: 8th layer
Ruled by Volisupula the Flensed Marquesse, lord of ostentatious finery. The layer itself makes you more evil the longer you stay there. Tieflings are immune.
Twelvetrees: 12th Layer
Definitely a place of horror, and a living example of why you can never, ever trust a demon.
Eons ago, some demons tricked some astral devas into having a meeting for the sake of peace. Basically, the powers from the Upper Planes saw the tanar'ri overthrow the obyriths, and thought maybe that the new fiends were "better" than the old ones. Big fucking mistake there: the demons turned on the angels, bound them to twelve of the biggest trees in the layer, and then performed a blasphemous arcane ritual that sacrificed them to the layer, allowing their eternal suffering to become fuel for all kinds of evil shit.
The angels can still be heard screaming, and a big altar now commemorates the site of the sacrifice, surrounded by twelve sickly pines that ooze some kind magically-infused slime. Evil-descriptor spells are Maximized and Extended automatically for free as a result of the power of the place. Demons make pilgrimages to the layer, to honor the screw job their kind put to the forces of good, and the overwhelming evil of the place is like a drug to the fiends, as the bask in a haze of quasi-religious ecstasy and basically don't give a shit what's happening around them, making it scarily easy for non-demons to wander around pretty freely (you only gotta dodge some chasmes that patrol the skies, maybe some kelvezus that look for intruders to murder).
But that's not all. See, someone figured out how to harness all that deliciously evil energy to create a new weapon of war: the ship of chaos. This horrible thing is basically made of flesh, bone, and spirit; it's hull seems to be comprised of some kind of twisted, thick, ropelike fibers, woven into an organic mass of mottled white and yellow, with translucent blue blisters along the flanks. They are powered by the annihilation of soul larvae... meaning that the ship itself absolutely destroys souls beyond recovery in order to operate. It can generate an "entropy field" almost the length of 5 football fields that either drives beings insane or simply repulses them, and shoots waves of force out of the mouths at the front and back. It can warp itself to travel through small portals, but this causes magic stuff onboard to possibly break unless it is made from the Abyss, and tanar'ri and their kin aren't particularly messed up by the warping.
The scaffolds for these ships dot the area around Twelvetrees. Six have been completed for sure. There was a seventh ship in the 2nd edition Planescape adventure In The Abyss, but it's highly likely that it was destroyed. The 3rd edition supplement FC2: Hordes of the Abyss notes another seventh ship is being built, which seems likely. In theory, these ships will not only be awesome weapons to use against the devils, but will mean the demons don't need the yugoloths to help them travel to Baator anymore.
And all this time, the angels keep screaming.
Blood Tor: 13th Layer
Steaming Fen: 14th Layer
Pleroma/Death's Reward: 17th layer
Ruled by demon prince Abraxas the Unfathomable. He has a roosters head and a bunch of snakes for a lower body. He's big on magic and the occult. Diovengia is his city which houses some of the best libraries in the entire Abyss.
The Sixth Pyre: 21st layer
Ruled by Prince Kardum, the lord of Balors.
Ice Wastes: 23rd layer
Kostchtchie is the resident Demon Prince. An infinite expanse of jagged mountains, glaciers and frozen tundras. Kostchtchie commands a big army of frost giants which he used to further "conquer" his layer, when he isn't siccing them on other demon lords for laughing at him, or conquering other tribes of frost giants on the Prime Material Plane.
Sholo-Tovoth/ Fields of Consumption: 32rd layer
Ruled by Demon Prince Turaglas, The Ebon Maw, who was spawned directly from the Abyss. A 100% pure demon and therefore envied by Orcus and Demogorgon for this (Demogorgon was a creation of the Obyriths, while Orcus was a former mortal) who joined against him and imprisoned him for a while. His goal is to devour and destroy, he has spawned his own breed of demons, the turagathshee. The layer itself, tries to eat anyone that enters it that's not either Turaglas or one of his minions, with mouths and tongues popping up everywhere. Its filled with millions of insatiable demons.
Azzagrat: 45th, 46th, and 47th Layers
Ruled by Graz'zt, demon lord of tyrants, manipulation, and, unofficially, blatant nepotism. There's a salt river that connects all three layers. Zelatar is a big, shiny, evil pastiche of the Emerald City of Oz that stretches across the three layers. Relatively well-behaved demons, not that it's saying much, as all of Grazz't's minions know that Grazz't torturing them to death for a minor screw up is the least he can do to them. Not a terrible place for a party, assuming it's the right kind of party.
Phage Breeding Ground: 53rd Layer
Ruled by Urae-Naas, a "female" slaad Demon Princess so bloated with eggs she can't walk anymore and has to drag herself along on her long arms and enormous tongue. Comprised from the interiors of the ever-rotting organs of her former boyfriend, the slain Primordial Ramenos. Iconic local feature: screaming, insane humanoids sewn into the walls begging ceaselessly for help before she gets around to implanting her offspring in their bodies. Created in 4th edition, and probably lost with the change to 5th edition seeing as how Slaad are Chaotic Neutral in all non-4 editions.
Torturous Truth: 57th layer
Ruled by Alvarez the Purging Duke, the head of the demonic Inquisition. His forces investigate the tanar'ri for any signs of lawful behavior. His torture is notorious throughout the Abyss.
The Demonweb Pits: 66th layer usually
The place where Lolth, the deity of the drow, and the rest of the drow pantheon, hangs out with her spiders. In 3e this was changed to be an entirely separate plane, though it's still connected to the Abyss.
Wells of Darkness: 73rd layer
A spa-cum-prison for some of the worst prisoners the plane could play host to. Jacuzzi tubs of black ink keep unspeakably powerful beings trapped beneath the surface, unable to get out, but perfectly conscious and able to communicate. It's amusing because the idea of an unbreakable prison on a chaotic plane constantly attracts break-in attempts by those who just want to prove otherwise.
Smargard: 74th layer
Merrshaulk rules here. He is the deity of the Yuan-ti snake men. Basically a nightmarish, evil, rainforest (one of several in the Abyss).
The Gates of Heaven: 77th layer
Actually not named ironically, it's apparently a gate to Celestia in the middle of a Chaotic Evil hell. Must be a really sturdy gate. Ruled by demon lords and brothers, Munkir and Nekir.
Abysm/The Gaping Maw: 88th layer
The realm of Demogorgon. Also known as "The Upside Down" thanks to Stranger Things. Pretty much a tropical nightmare, with demon- and demonic-disease-infested jungles and a roiling ocean. Dagon, his special friend and mentor, lives in his basement.
Shadowsea: 89th layer
Ruled by Dagon one of the few obyrith lords still part of the establishment. It's an underwater realm without a surface although it connects to the 88th. Filled with myriads of aquatic demons.
Demonwing: layer unknown
An entire layer of the Abysm transformed into a crazy demonic pirate ship by Demogorgon that can move freely about the planes.
The Guttering Grove: 90th layer
Ruled by Ilsidahur, the Howling King, who's a bootlicker to Demogorgon. He leads the bar-lgura, these orangutan looking demons, as well as these winged gorilla looking guys. The Guttering Grove was recently subsumed into Abysm by Demogorgon as punishment for Ilsidahur screwing up an invasion of Arcadia, though Ilsidahur is apparently either too unaware, too uncaring or too stupid to notice.
The Mind of Evil: 111st layer
Ruled by Prince Sch'theraqpasstt, the Serpent Reborn.
Thanatos: 113th layer
Its as much undead as demonic. Orcus's crib. He spends most of his time chilling here not doing things.
Slugbed: 128th layer
Lupercio the Baron of Sloth rules here. It's a tropical, mostly overcast realm filled with lush forests and coral reefs filled with all manner of demon gastropods. Because Lupercio is too busy spending most of his time sleeping, where his perpetually darkness-shrouded form is perpetually parasitized by shadow demons, and too spending what precious little waking hours he has maniacally doing something, the demon gastropods of Slugbed do not recognize his authority, and, instead, do their own thing, i.e., eating the scenery, each other, and intruders too stupid to understand the threat posed by demon gastropods until they get eaten. An army of angels has secretly constructed fortresses in the clouds above Slugbed, and eventually intend to use their fortresses here to stage attacks on the demons of the Abyss.
Outcast's End: 137th layer
Ruled by the exiled and outcast Azazel, Prince of Scapegoats.
Lifebane: 142nd layer
Hollow's Heart: 176th layer
Ruled by Fraz-Urb'luu. Fraz-Urb'luu pissed off virtually all of the other demon lords by learning how to summon them in order to humiliate them in front of his sniveling minions. This led to the demon lord being forced to take a sabbatical in the dungeons of Oerth while lesser Lords moved in, turning the place into a demonic continent of crazy shit. Including a jungle of skin, where trees are hairs sprouting from the ground. A desert made of grains of clotted blood and a city shrouded in powerful illusions to make petitioners think everything is happy and safe, so the demons can take it away piece by piece.
The Rotting Plain: 181st layer
Ruled by Laogzed the god of the troglodyte. Here they archive everyone's browsing history, purchase's, and other personal information forever.
Vulgarea: 193th layer
Ruled by demon princess Eshebala the foxwoman and wolfwere goddess.
Shedaklah, the Slime Pits: 222nd layer
The Dreaming Gulf: 230th layer
A phantasmal dark and wind-swept realm with no ruler. This is where the dreams of evil gods go when they die, slowly being given form by the Abyss.
Palpitatia: 241st layer
Grankhul and Skiggaret, the bugbear gods, rule here.
The Scalding Sea: 245th layer
An entire ocean of acid with islands of black glass. Probably deserted, the one island town is empty, with its former occupants encrusting the town's walls while the town's fountain screams eternally and sprays yet more acid.
The Hidden Layer: 248th layer
A huge thunderstorm-ravaged wasteland. Was ruled by Demon Prince Eltab, until he was summoned into the Prime Material and bound there, also sucking small portions of his realm with him to Faerun in the form of demoncysts and leaving his subordinates to fight amongst themselves over control of the rest.
Durao: 274th layer
A ruler-less layer dotted by military encampments and demon barracks interconnected by iron roads that snake through the otherwise swampy environs along the River Styx. It was from here that most of the demon armies staged before departing to wage the Blood War in Gehenna.
Feng-Tu: 300th layer
The Broken Scale: 333rd layer
Fortress of Indifference: 348th layer
Rough terrain with fiery skies. An evil 200 foot tower is the main attraction. Its the home of outcasts, half-fiends, tieflings, etc. that turned their backs on the Blood War. Its particularly anarchic. Tapheon, a barely held together demon, tries to rule here but mostly goes around torturing random beings.
Arch of Eternity: 359th layer
Ruled by Eldanoth, the Prince of Crime. He once served under Orcus but left after Orcus was overthrown for a time, now his servants sabotage Orcus's plans. He's worshiped by criminals. The realm is, ironically, a huge, but finite plane of fire and snakes with a copper fortress at its center.
White Kingdom: 421rst layer
Ruled by the King of Ghouls, who, depending on the author, is either a toady of Orcus, a hostage-turned-minion of Yeenoghu, or an undead god who's free to do his own shit.
Death Dells: 422nd layer
Ahriman-abad: 452nd layer
Ruled by Ahrimanes, the Chief of the Cacodaemons.
Guttlevetch: 480th layer
A sea eternally swept by perpetual typhoons and hurricanes, its beaches of blood are littered with innumerable shipwrecks. Was ruled by Zuregurex, Lord of the Drowned, but he seriously fucked up when he tried to invade Demogorgon's layer. Zuregurex fled to the 245th layer to escape retribution.
Mansion of the Rake: 487th layer
An entire layer stylized as a perpetually shifting baroque-style palace. Ruled by Kanchelsis the god of vampires, born of the blood of the elven gods. His primary servants are vampires, drow, and the occasional crazy birds in his aviaries. His live-in boarders-turned-sort-of-minions are a trio of crazed blood fiends, Memnul, Dagrobard, and Vonce, who are so unpleasant, they apparently scare even Kanchelsis shitless.
Noisome Vale: 489th layer
Tarnhem is the official ruler here, though he's left for a while to go and hike Mt. Everest to find himself or something. The layer itself is mostly volcanic, creating a poisoned and acidic atmosphere. However, a deep canyon carves its way through the layer which is infested with worms. These worms thrive in the acidic air, breathing it in and expelling breathable air as a waste byproduct. Tarnhem's estate is built along the ravine, and his servants still occupy it awaiting his return.
Torremor: 503rd layer
An aerie, built out of bridges, buildings and junk, floating in a void, and inhabited by vrock, chasme and other flying demons. Officially ruled by Pazuzu, though, he has, more or less, abandoned it to his ex-girlfriend, Lamashtu. For a while they were a disgustingly close couple, then Lamashtu betrayed him, and then they broke up when he ate out her eyes and impaled her on top of a tower at the very top of Torremor, where ever that is. He's more or less forgiven her, but still can not be assed to un-impale her.
Occipitus: 507th layer
Adimarchus, Prince of Madness, is the prince. He is a fallen Celestial and thus this layer is actually a fragmented piece of Celestia (the Seven Heavens)that fell with him. Demons avoid this layer all together, its filled with ruins and basins. Adimarchus fought a big fight against Graz'zt and lost at one point. He is imprisoned in Skullrot in Pandemonium, and has a split personality, one angelic, one demonic, which is why he's called "Prince of Madness."
Shatterstone: 524th layer
Ruled by Vaprak the ogre deity.
Vudra: 531st layer
Fleshforges: 558th layer
Ruled by Demon Prince Dwiergus, the Chrysalis Prince. He has control over the shaping of demonic races. Probably older than Pale Night. The Father of Demons in some ways. A mentor to Baphomet who taught him how to create new demons.
Prison of the Mad God: 586th layer
Ruled by Diinkarazan, one of the two gods of the derro.
Goranthis: 597th layer
Shubgottia, The Endless Maze: 600th layer
Ruled by Baphomet, Prince of Beasts. He lets Pale Night, a ghost looking entity, the mother of demons allegedly, have a castle here as well though she rarely does anything. Lyktion is his palace and at his Tower of Fucking Science he experiments and creates new demon breeds and such. He has vast armies of beastmen looking demons and is revered by the minotaurs. He is smart, savage, one of the top tier princes, and is not to be fucked with. He began as a mortal creature, either as a beast that lived as a man or a man that lived as a beast, and was cursed by the gods, though obviously he made the best of it.
Conflagratum: 601rst layer
Ruled by Alzrius, Lord of the Flowing Flame. He usually manifests himself as a pillar of fire and leads his legions to the burning of all bitches.
Zionyn: 663rd layer
Ruled by Obox-ob, Prince of Vermin, an ancient obyrith demon. He is allegedly the last surviving aspect of the old Prince of Demons. He hates the tanar'ri and wants to ethnically cleanse the Abyss from them, as well as overthrow Demogorgon.
The main race in the Abyss are demons. There are four different categories of demons: The Tanar'ri, the Obyriths, the Loumaras, and everything else. The Tanar'ri are the only ones who ever get shit accomplished, and are somehow the most numerous in spite of the fact that, again, there are an infinite number of demons. Most of the demon princes are Tanar'ri, though there are some Obyriths.
The petitioners in the Abyss are called manes, and become a low caste of Tanar'ri. If they survive for a very long time, they can be promoted up into the ranks of the not-worthless, and even to demon lords if they're cunning enough. This is how Orcus got his start.
Most of the chaotic evil deities live in the Abyss as well, for obvious reasons, including the aforementioned Great Mother and Lolth (depending on edition). Deities here are also called demon lords, because that's generally just a title and not any kind of useful disambiguation. Also because there's plenty of layers to go around so if you've got the power you might as well rule one.