Abyss
The Infinite Layers of the Abyss is the Chaotic Evil plane in Dungeons & Dragons great wheel cosmology. It's home to an infinite number of Demons, the Chaotic Evil fiends.
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.
Notable Layers
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:1rst 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.
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.
Pleroma/Death's Reward: The 17th layer of the Abyss. 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.
Ice Wastes: 23rd layer. Kostchtchie is the prince. Has a big frost giants army.
Azzagrat: Tree layers, the 45th, 46th, and 47th. Ruled by Graz'zt who's a fucking devil not a demon! He was sent on an assault by Asmodeus and apparently decided to just make his own realm of what he conquered. Why demons serve him is beyond reason, probably shitty writing. He has a salt river or some shit. Zelatar is his stupid big city that stretches across the three layers.
The Demonweb Pits: The 66th layer usually. The place where Lolth, the deity of the drow, hangs out with her spiders. In 3e this was changed to be an entirely separate plane, though it's still connected to the Abyss.
Smargard: 74th layer. Merrshaulk rules here. He is the diety of the Yuan-ti snake men. Basically a nightmarish, evil, rainforest.
Abysm/The Gaping Maw: 88th layer. The realm of Demogorgon. Pretty much a tropical nightmare, with demon infested jungles and a roiling ocean. Dagon lives in his basement.
Thanatos: The 113th layer of the Abyss. Its as much undead as demonic. Orcus's crib. He spends most of his time chilling here not doing things.
Hollow's Heart: The 176th layer of the Abyss. Ruled by Fraz'Urb'luu.
Slime Pits: 222nd layer. Juiblex the Slime lLord and Zuggtmoy, the Lady of Fungi rule here. Obviouslly a disgusting place.
Indifference, Fortress of: 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. Tapheon, a barely held together demon, rules here.
Noisome Vale: The 489th layer Tarnhem is the official prince here though he's left for a while to go and hike Mt. Everest to find himself.
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. He fought a big fight against Graz'zt and lost. He is imprisoned in Skullrot and has a split personality, one angelic one demonic.
The Gates of Heaven: 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.
Inhabitants
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.