Black Abyss

The Black Abyss is where all demons are spawned from.

Location

Being a place that spawns demons, and where demons return when killed. It's likely located somewhere in the Burning Hells, but not necessarily so, since it could, in theory also be the spawning place of angels. In either way, it's separate from the Void, which is more like a "limbo" between planes and places of existence, where beings can be trapped. Lilith is an example of a demon trapped in the Void.

References

It's primarily Tyrael that brings information about the Black Abyss:

Tyrael: "For his transgressions, Izual's spirit was bound within the form of a terrible creature which was summoned from the Abyss. His maddened spirit has resided within that tortured husk for many ages now." (In-game dialogue)

Tyrael: "Diablo and Mephisto have been banished back into the Black Abyss that spawned them and the corrupted Soulstones are no more." (In-game dialogue)