The Abyss is a alternate dimension that is loosely connected to the cycle of death and rebirth that the Soul Society and the World of the Living make up. It is the central point of the Abyss Chapters Filler.
The Abyss is an alternate dimension that lies somewhere outside the cycle of death and rebirth that souls are a part of and helps maintain balance in the universe. Any Soul or Hollow slain by a Quincy, Bount, or Fullbringer is sent to The Abyss, following the laws of balance that energy cannot be created or destroyed. It was believed that souls slain without the use of a Zanpakuto were completely destroyed but what was discovered is that these souls are actually sent to The Abyss, although this fact is not taught or even spoken of. The world ending event spoken of when there is an imbalance in souls between the World of the Living and the Soul Society is actually caused by having an imbalance between The Abyss and these two worlds combined. If either the World of the Living or the Soul Society fall to far out of balance they will cave in, imploding into The Abyss which lies somewhere between the two worlds.
The Abyss is exactly what it sounds like, a vast area of nothingness. This lack of substance is what causes Souls who are sent here to turn into Dark Souls. It is believed that it is not something in The Abyss that causes transformation but something it lacks. Reishi, Reiatsu, and other Souls are what keep Souls from converting into Dark Souls, each Soul keeps other Souls in balance in combination with the spirit energy present in the air of The Soul Society, The World of the Living and even Hueco Mundo. A lack of exposure to these elements causes Souls to degrade and decay into Dark Souls.