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.
The Grand Abyss/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 demon princes co rule this layer. The Grand Abyss is sometimes the 4th layer and Pazunia is the Styx shorelines.
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.
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.
Skin-shedder: 8th layer
Ruled by Volisupula the Flensed Marquesse. The plane itself makes you more evil the longer you stay there. Tieflings are immune.
Twelvetrees: 12th Layer
Originally intended as a neutral ground for fiends and celestials, until the Tanar'ri double crossed the Angels and turned them into twelve trees that constantly scream distractingly and make normal conversation impossible, circled around a single altar. The tiny realm is strongly chaos & evil aligned, while anyone standing on the altar maximises and extends any evil spells they cast.
Blood Tor: 13th 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 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 enormous expanse of jagged mountains, glaciers and frozen tundras. Has a big army of frost giants.
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 a tries to eat anyone that goes by it that's not under Turaglas, with mouths and tongues popping up everywhere. Its filled with millions of insatiable demons.
Azzagrat: 45th, 46th, and 47th Layers
Ruled by Grazz't! There's a salt river or some shit. Zelatar is a stupid big city that stretches across the three layers. Relatively well-behaved demons, not that it's saying much. 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.
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.
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 infested jungles and a roiling ocean. Dagon 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.
The Guttering Cove: 90th layer
Ruled by Ilsidahur, the Howling King, who's a bootlicker to Demogorgon. He leads these orangutan looking demons, as well as these winged gorilla looking guys.
Demonwing: layer unknown (and probably irrelevant)
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.
Outcast's End: 137th layer
Ruled by Prince Azazel.
Lifebane: 142nd layer
Ruled by Chemosh, the god of undeath in Krynn.
Hollow's Heart: 176th layer
Ruled by Fraz'Urb'luu. The demon lord took a sabbatical in the dungeons of Greyhawk and lesser Lords moved in, turning the places into a daemonic 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 goddess.
Slime Pits: 222nd layer
Juiblex, the Slime Lord, and Zuggtmoy, the Lady of Fungi rule here. Obviously a disgusting place. Sometimes the 528th layer.
Palpitatia: 241st layer
Grankhul and Skiggaret, the bugbear gods, rule here.
The Hidden Layer: 248th layer
Ruled by Demon Prince Eltab. Its a huge thunderstorm filled wasteland.
Feng-Tu: 300th layer
Ruled by Tou Mu and Lu Yueh, gods from the Chinese Mythology.
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 a huge plane with a copper fortress.
White Kingdom: 421rst layer
Ruled by the King of Ghouls.
Seeping Woods: 422nd layer
Ruled by Yeenoghu, Demon Prince of Gnolls.
Ahriman-abad: 452nd layer
Ruled by Ahrimanes, the Chief of the Cacodaemons.
Mansion of the Rake: 487th layer
Ruled by Kanchelsis the god of vampires. His primary servants are the blood fiends Memnul, Dagrobard, and Vonce.
Noisome Vale: 489th layer
Tarnhem is the official prince here though he's left for a while to go and hike Mt. Everest to find himself.
Torremor: 503rd layer
Ruled by Pazuzu. Mostlly avian demons. Full of beams, ladders, towers, ropes, etc.
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 and has a split personality, one angelic one demonic.
Shatterstone: 524th layer
Ruled by Vaprak the ogre diety.
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.
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.