A dark and formless void, in an already dark and sad world. It's accessed via the New Londo Ruins after you lower the water level. It serves as the arena for the Four Kings boss battle and, once they're defeated, is also the home to Darkstalker Kaathe, the leader of the Darkwraith Convenant.
Before you begin, please note that to enter The Abyss and not die you must be wearing the ring you got from killing the Great Grey Wolf Sif in Darkroot Garden - the Covenant of Artorias. Also, to reach fog gate that leads to the The Abyss you will have to have lowered the water level in New Londo Ruins. For further details on how to reach the fog gate that leads to The Abyss, please refer to the New Londo Ruins walkthrough.
Once you reach the fog gate, it's worth knowing that there is a summon sign for an NPC nearby - Witch Beatrice - who can help you with the Four Kings boss fight. The sign will only appear if you are in human form and only if you already utilised her for the Moonlight Butterfly boss in Darkroot Garden. To find her sign, look for a large pillar to your right when looking at the fog gate - you'll find her sign around the otherside of the pillar. It's a good idea to kill all Ghosts and Darkwraiths in the area prior to summoning her.
When you go through the fog gate you'll be at the top of a spiral staircase. If you haven't equipped the Covenant of Artorias yet, then now is the time to do so. Travel down the stairs and you will find that it just ends rather suddenly, leaving you in a free-fall into blackness, before landing at the bottom. Welcome to The Abyss - the first of the Four Kings will appear in a moment.
Boss Fight: Four Kings
After you kill the Four Kings, you do not need to wear the Covenant of Artorias anymore, although be warned that you still need it equipped to help with the Four Kings fight in other players worlds. Also, a bonfire appears after they are dead - this bonfire will let you warp, even if you do not have the Lordvessel yet.
If you have the Lordvessel though and didn't go to Kingseeker Frampt in Firelink Shrine with it, then you'll also find Darkstalker Kaathe beside the bonfire. He'll take you to the Firelink Alter to place the Lordvessel and will also allow you enter the Darkwraith covenant - read up on this covenant to decide if you want to join. NOTE: Be aware that placing the Lordvessel with Kaathe will anger Frampt, and you will no longer be able to avail of his services for this playthrough.
Once you're done here the next stop is The Duke's Archives, so warp to the 'Anor Londo' bonfire to continue the main quest.