At the end of all things, it sits and waits for all things to fall into its maw. It is the ultimate hole, the ultimate nothing, the void which haunts the dreams of even Fuyutsuki and Anno.
More pragmatically, the Abyss is a big nasty hole in creation next to the Courts of Chaos. Some theorize it may in some way have been produced by the actions of the Logrus, for in every known universe, it lurks near the Logrus, and it seems to connect to every universe as well.
Still, the Abyss is not quite as true a void as one might think. While every known power fails there if one goes very deep at all, beings seem to either exist within the Abyss, or perhaps simply use it as a highway to visit our Universe from other ones. The Abyss Monks study its mysteries and seek to unite with its power. The Abyss Pirates use it as a highway to raid shadow, for in some ineffable way, it seems to touch all that is. And the Abyssal Demons seem to call it home (or perhaps, like the Pirates, it is a road for them as well).
Some people believe that the Abyss is itself a primal force whose power can be tapped; the existence of Monks, Pirates, and Demons, would seem to demonstrate this. It is rumored that Annadil had an assistant Mamiya, who possessed this power and used it to fling the White Knight into the Abyss.