Tl;dr ver.:

The Void is the sad, shattered remnants of the Thirteenth Reflection after Igeyorhm's machinations tipped the world too close to darkness. The inhabitants went mad with the power of Auracite, dooming the land to have all of its aether crushed and compressed into a singularity. What remains of the realm is little more than a few sparse fractions of barely hospitable terrain, and the former denizens have been warped into monstrous voidsent that exist outside the cycle of life and death (since the Void has no Lifestream to speak of).

The void is simply shorthand for the Interdimensional Rift that exists between all Final Fantasy titles, chiefly for explaining how various characters (Lightning, Gilgamesh, Shantotto, Iroha, etc.) from other titles make appearances here.