Makes ya think - you're all just sinkin' - body and soul - deeper an' deeper... into the ABYSS!!
--Abyss
When Legion, the mentally unbalanced mutant son of Professor Charles Xavier and Gabrielle Haller, traveled back in time in an attempt to kill Magneto, he accidentally killed Xavier instead, creating a splinter universe known as the Age of Apocalypse. In that reality, mutants became the dominant species of the planet. Apocalypse rose to power enslaved humanity.
Little was known of Abyss' life before he became a Horseman of Apocalypse. It was said Abyss was experimented upon in Sinister's labs after escaping he killed the Horseman Bastion. Rather than have him killed, Apocalypse was impressed and appointed him as his new Horseman[1].
Abyss was assigned to prevent the evacuation of humans from Maine to Europe by the X-Men and Sentinels[2]. However, he decided he'd rather capture Quicksilver, and kidnapped a young boy as bait. Storm intervened, causing this plan to fail[3].
Abyss was then entrusted with overseeing the Madri and Shadow King's interrogation of Bishop[4]. The X-Men were dispatched to save Bishop, which resulted in another battle with Abyss. Abyss mocked Banshee and caught him in his void. Banshee's sonic screams ripped Abyss apart from within, apparently destroying him[5].
Many years later, Dark Beast attempted to bring Abyss back to life after having preserved his corpse. His attempt was sabotaged by Fiend, though the Dark Beast's experiments resulted in many other deceased mutants being brought back.
Abyss (AoA) has a slightly different appearance but essentially the same powers and is "evil". Abyss (AoA) version of the character appeared prior to the 616 version.
Abyss (AoA) was a nihilist with a warped sense of humor.
The final boss in the video game "Marvel vs Capcom 2" goes under the name Abyss, although the two bear no real similarities apart from the name.