The Abyss is a binary pair of massive black holes located near the space that Old Miltia once occupied. In reality, Old Miltia was sucked into the black holes immediately after the Miltian Conflict, due to Joachim Mizrahi's activation of the Original Zohar. In order to reach Old Miltia, the Y-Data is needed to find the path through the Abyss.
In Episode II, the U.M.N. gate to Old Miltia is unlocked by Albedo Piazzolla after he retrieves the codes from MOMO's Y-Data. After Old Miltia emerges from the Abyss, the two black holes vanish and do not reappear again.
Episode I's U.M.N. Database makes mention of the fact that the term "Abyss" can also be used to refer to Hell. This also adds to Joachim Mizrahi preaching Revelation 20 from the Bible before Miltia fell into the Abyss.