The Black Abyss is the apparent birthplace of demons. No-one knows exactly what the Abyss is, but it is believed that once something is banished to the Abyss, it can never return. Of note, a "terrible creature" was summoned from the Abyss to bind the spirit of Izual.
During the return of the Prime Evils, the spirits of Diablo and Mephisto were (supposedly) banished to the Abyss after the destruction of their soulstones at the Hellforge. However, as aspects of their essence lingered in Sanctuary, they were able to be 'marked' by Adria, preparing them for absorption into the Black Soulstone.
The Abyss is not to be confused with the Void.