Loveless is an epic poem of unknown origins, perhaps dating back as far as to the time of the Ancients. It's missing the final act, and so the meaning of the story has been debated by scholars for quite some time, and many people have their own theories and conclusions. Hojo even researced it for some time, but in the end believed it was nonsense with no factual basis. The greatest question regarding the poem is what the Gift of the Goddess is.
One of Genesis' hobbies is researching the poem, and he becomes fairly obsessed with the concept of the Gift of the Goddess, to the extent that during the course of the game, he tries to recreate the events of the poem in order to figure out what it means.
In the end, it's revealed that there is some factual basis to the tale, and the Goddess is a real entity, known as Minerva, which is similar to a summoned creature, in some regards. Minerva is the collective will of the Lifestream, so to speak. When Genesis is defeated by Zack in the Lifestream-flooded caverns beneath Banora, he essentially comes to his senses and regains his pride as a SOLDIER, coming to the conclusion that his true interpretation of the "Gift of the Goddess" is the ability to carry out his duty.
Therefore, his strong drive to overcome degeneration, and the innevitable death it will lead to, summons Minerva to him. Minerva judges him, and the will of the lifestream is that he has much left to do, and cures his degeneration, allowing him to surmount death and carry out his duty.
Genesis eventually decides that, with Angeal and Sephiroth dead, he is the only one left to protect the Planet, so he seals himself in a cavern beneath Midgar to await for a crisis to threaten the world and awaken him. So, in a bit of a twist, his seemingly forboding appearance at the end of Dirge of Cerberus should be reinterpreted, as he's actually emerging to protect the Planet, whatever that entails.
I'd suggest checking out the translations at
http://ultimania.ff7compilation.net/, especially the CC Scenario Q&A and CC Complete Guide Goddess information.