The Great Rift, also known as Cicatrix Maledictum (which more or less means the Cursed Scar), Gork's Grin, Mouth's Ruin, the Dathedian... is a massive chain of Warp-storms that has tore realspace in half after the destruction of Cadia and its pylons by the Warmaster of Chaos, Abaddon the Despoiler. In its current state, it has divided the galaxy into two halves, plus a couple of independent warpstorms in certain areas. This has obviously meant bad news to every major faction in the galaxy other than Chaos (and maybe orks, because now there are more spiky gits to krump), and has especially affected the Imperium of Man, dividing its territory into two halves almost isolated from each other: the part where the Astronomican still shines normally, and the part where its light can barely reach. This half of the Imperium usually gets the name Imperium Nihilus (or the Dark Imperium), both because it's been darkened by the Great Rift and because it's becoming an increasingly bad place to live in, due to Warp shenanigans and xeno attacks.
So what exactly started it all?
During the last couple of centuries, the tides of the Warp had been more and more erratic and violent, making space travel more and more dangerous. It's been widely believed that Abaddon the Despoiler's dark crusades had the secret objective to destroy a series of ancient structures that kept the Warp from overflowing into the materium. During the 13th Black Crusade and its final assault on Cadia, Chaos forces managed to destroy the last big series of pylons, the ones that prevented the growth of the Eye of Terror. The destruction of those last pylons alongside the rest of the planet started a chain reaction that formed multiple warpstorms throughout the galaxy. Abaddon's original plan was, in theory, cause a warpstorm big enough in Holy Terra's direction to either destroy the planet and the Emperor of Mankind or to invade with all the forces Chaos could muster, assuring the destruction of the Imperium. However, these massive warpstorms started joining with each other, and instead of growing into the direction of the Segmentum Solar, it went into the Maelstrom, consumed the Galactic Core, then moving into a straight line and dividing the galaxy neatly in two.
Despite supposedly destroying the Cadian pylons, Abaddon still managed to get a hold of some from somewhere, either from the wreckage or dug up from somewhere else. He managed to actually transport them in giant grand cruisers to various worlds in the Segmentum Solar, originally part of a plan to becalm the warp-space around Terra and isolate Roboute Guilliman while the High Lords of Terra tried to depose him, this was only thwarted because the Sisters of Silence and the Adeptus Custodes performed a rogue operation and exposed the plot before it was completed. Dante is then assigned by Guilliman to be the regent of the Dark Imperium.
What does this mean for the galaxy
It means bad news. Horrifically, apocalyptically bad news.
Imagine the danger that the Eye of Terror represented to the galaxy back when it was just a single region in realspace. Now imagine that same danger multiplied by a hundred and spread around most of the galaxy. The Eye of Terror spreads the madness and dangers of the Warp into realspace at twice the rate, and affects a much, much bigger area than before. Hundreds, if not thousands of systems were immediately sucked into its warpstorms, with all the horrific consequences implied from that. Not to mention all the space-time distortions effects that an event like this could mean, with some planets frozen in time while other lived full millenniums in the blink of an eye, some planets changing place and appearing out of nowhere, or just disappearing...you get the idea. It's gotten so bad that even in-universe any kind of objective measure of time is no longer meaningful.
Each faction, however, has reacted to it differently.
- Chaos is obviously the one profiting from this, although after the birth of the Great Rift, Abaddon's 13th Black Crusade started to slow a bit due to the desire to pillage and burn for their own gain, instead of following an organized plan. But let's be fair, this is Chaos we're talking about- it's a miracle they even followed the plan as long as they did. Millions of Chaos pirates assault every planet they can, while the Chaos Gods try to occupy more territory than their rivals. If it weren't for the Great Game monopolizing their attention, the Chaos Gods might have been able to completely wipe out their opposition on the spot.
- It's important to realize that Chaos is much more than Abaddon's own agenda. Whatever his goals might have originally been, the fact that daemons can more easily be brought into realspace is a BIG deal. Almost as soon as the Great Rift erupted Daemons of Khorne(without Marines, or even the approval of the other three Chaos Gods) managed to attack Terra, and Ultramar got a full-blown Nurgle/Death Guard invasion later on.
- Chaos Marines have always used warp storms to conceal their movements, while they may not be the most safe or reliable of places to hide, Chaos forces have a notable advantage when it comes to navigating them over everyone else. It is notable, however, that the traitor legions considered the Eye a "prison" as much as a haven, but they seem to be better able to leave the Rift more easily than they could leave the Eye of Terror.
- The Imperium of Man almost loses half of its territory, only managing to get in contact with the Imperium Nihilus by two warp corridors, constantly attacked by daemons. The Indomitus Crusade was launched during the aftermath of the Great Rift's birth, trying to push back the Chaos hordes pouring from it. While Roboute Guilliman's leadership was able to stabilize the situation in the Dark Imperium for the time being, he expects that holding onto it will be difficult even for him.
- The Orks are having a zogging good time, smashing, crumping and chopping all of the spiky gits and other fun things coming from the Rift. Indeed, they interpret the Great Rift as a divine miracle from their gods and a sign of their upcoming arrival on the mortal plane to usher in the final WAAAAGH! They've also recently taken up the habit of deliberately flying into it in the belief that the warp storms will scatter them somewhere else in the galaxy. Ghazzy is still trying to get the GREAT WAAAGH! going, but he's so far stomped the Tyranids of the Octarius system real good and won the war, so he's making some progress. Seeing as how he's somehow been able to be in multiple places at once, it may be possible that Gork and Mork gave him another power-up somewhere along the line.
- The Eldar are trying to find a way to repair realspace, the dangers of the Immaterium being a very real threat to them. Travelling through some sections of the Webway has become impossible, and some even fear the Cicatrix Maledictum could even end up breaking it. As such, there has been a massive collaboration between the different Aeldari groups in an effort to contain the warprift (even the Dark Eldar, who no doubt profited from all those undefended human planets before the daemons arrived), with the ultimate effect on this being the birth of the Ynnari and its "alliance" (along with Craftworld Alaitoc) with the Imperium of Man.
- Necrons are more or less unaffected by the Warp, having no soul and such, but some Necron Lords have become interested in stopping the Rift's growth as this is a threat to the ones attempting to rebuild the ancient Necrontyr empire. Plus if all the organics are gone or corrupted by the warp, how are they suppose to get flesh-and-blood bodies again? Some Necron Lord's empires have been expanded during this, too.
- The pylons that held Cadia together were originally Necrontyr. Necron Crypteks are frantically trying to recover and construct additional pylons to pin the universe back together, although this has been a slow process and often involves scrape-ups with the Mechanicum.
- The Tau, trying to take advantage of the situation, launched a full expansion sphere equipped with their brand new Warp drives to prey upon the undefended planets they could. And immediately lost it due to said Warp drives opening a rift in the Warp. Contact was later re-established with the Fourth Sphere, but it's suggested their time stuck in the Warp may not have been good for their sanity. The fact that the Tau still don't fully understand what Chaos is means bad news for the short term safety of their empire. Especially since another big Chaos force is headed their way.
- The Tyranids have been hit hard by this. The warp storms blocks most psychic light in the galaxy, so they have lost track of thousands of potential meals, and some are travelling blind. A couple of splinter fleets have probably been lost into the Warp by the sudden warpstorm. Hive Fleet Leviathan managed to reach Baal, but not before Khornate forces of Ka'bandha also launched an attack on the system and expressed his unwillingness to let the bugs steal his chance for revenge. After fighting daemons, the Blood Angels and Guilliman's reinforcements, Hive Fleet Leviathan has been reduced to a collection of splinter fleets like Behemoth and Kraken before it. This, combined by the fact the ‘nids lost against Ghazghkull Thraka in the Octarius War, means that, as of now, there is no major Hive Fleet threatening the galaxy, only relatively harmless (by tyranid standards at least) splinter fleets. This, however, has not discouraged the Great Devourer, and from the remains of all splinter fleets around, some new Hive Fleets have begun to emerge, more and more specialized in fighting daemons and Chaos elements. Hive Fleet Kronos in particular has become infamous for its success rate against daemons through massive long range firepower and a supercharged Shadow in the Warp. Hive Fleet Tiamet is also up to something, building a giant living structure in a backwater region of Ultima Segmentum which nobody else can tell what it is (although some speculate its a rally beacon for the Hive Fleets, which can be trouble for the galaxy as this will be another staging area for the Nids to use)
So basically everyone but Chaos and arguably the orks who are loving all the fighting have been fucked in one way or another.