Avalon (or Heaven, The Afterlife, etc.) is a paradise realm separate to Eternia where the Angels and the enlightened of the world live in tranquility forever. Very little is known about Avalon other than it is the intended final home for all Souls.
A soul ascends to Avalon once it has reached its spiritual apex; that is, a point where it is no longer capable of learning from its continued experiences and lives in Eternia.
Before the Archangel Kraus Eternia forged the world as humans know it, he created the Stars and Avalon. The stars were an integral part of a celestial system known as the Life Stream - a spiritual superorganism to be the heart of Eternia and indeed all living beings. Avalon was the final resting place for souls that had learned all there was to learn from Eternia. It was also intended to be a safe haven for the Angels, a true paradise in comparison to the world which they had came from: Atmos.
Kraus overestimated his control over creation in the end, and his power was depleted before he could finish the creation of Eternia. This destroyed his body and sent his 300 angels into a state of disarray. In his absence, the Angels established a new government to preside over both Avalon and Eternia - The Divine Council. Lead by the High Angel Azrael, it served to protect and guide Humans to greatness. The Angels vastly misunderstood the nature of humanity, however, and were lead to panic when the humans displayed murderous qualities of that of the Akuma of Atmos.
The panic caused a widespread implementation of totalitarian laws to keep humanity in check. Eventually, Eternia rebelled against Avalon and ignited an age of global-scale conflict known as the Divine War.
After Azrael's falling and attempted genocide of the human race, Kraus at last had returned and felled Azrael in combat. Perhaps horrified by what had transpired in his absence, he ordered all Angels to return to Avalon indefinitely. Centuries pass, and eventually Avalon and the Angels themselves fade to nothing but myths and tall tales.