An Abyss is a pit which leads deep underground with multiple fissures branching from it. Any monsters spawned near an Abyss will be weakened by it.
Defeating these weakened monsters will cause the fissures to close.
Once the fissures have closed all the way to the pit, the pit will activate and spawn a large number of Abyssal monsters. Defeating these monsters will close the pit.

Each closed pit has a chance to spawn an Abyssal Trove which can grant pieces of Preserved Bone to craft onto your Items. The final Abyss in the area has a chance to instead open an underground dungeon called an Abyssal Depths.

There are three separate groups of Abyssal Monsters: the Lightless, the Blackblooded and the Legion of the Pit, each area generally contains one of these groups.
The rarity of the monsters spawned depends on the rarity of the slain weakened monsters and the emerging Abyssal will steal some or all of the modifiers from them.
Any of the modifiers stolen by Rare Abyssal can be upgraded to Abyssal Modifiers.