Refers to a Heroic Spirit once again materializing in the world with a physical body. Rider’s wish is to reincarnate in a physical body and once again conquer the world. Gilgamesh reincarnates after bathing in the black mud of the Holy Grail. This is how Gilgamesh manages to remain in the real world for ten years and participate in the Fifth Holy Grail War.

Fate/Zero Animation Guide II: Glossary of the holy grail war II