Black Abyss

From Diablo Wiki

The Black Abyss is where all demons are spawned from. Note that the Void is separate to the Abyss. The Void is more like a place where beings can be trapped in (like Lilith), while the Abyss is where demons are actually spawned from and where they return to when they die.

We don't yet know if angels are also spawned from here or somewhere else.

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)