The Abyss is a realm that exists somewhere outside the human dimension. It is the home and prison to The Corrupted. Sometime in The Abyss, there was a war between The Corrupted and their slaves. It is assumed that the Corrupted won this war. During this war, a weakened spirit managed to escape The Abyss and entered the human world.
In Splatterhouse (2010), doorways into the the Abyss can be opened through human sacrifices. One such example is when the Terror Mask used its host, Rick Taylor, to sacrifice ten thousand lives in order to open a portal.
The Abyss was first seen in Splatterhouse 2, where it is depicted as the land of the dead. It is identified in the Japanese manual as a specific place where particular rebellious beings are contained as an everlasting purgatory. The seal on it in Shin Splatterhouse was opened by Rick to return Jennifer to the real world, although monsters leaked from it and led to the events of Splatterhouse 3. West's writings refer to it as the void in both games, and the Terror Mask is at odds with the Evil One, so it is likely the same world.
In the works of H.P. Lovecraft, he uses the word "abyss" multiple times. This could be where the writers of Splatterhouse (2010) got the name from, as they took several Lovecraft inspired themes.