Some time prior to the Dark War, the Drive Soul Eater had been parasitic, latching onto different humans across the world. Clavis Alucard dedicated much of his time to taking out its wielders. It eventually found itself in the possession of Saya Terumi, who then wiped out the entire Terumi branch family of the Amanohokosaka Clan. Saya was bound for years by Mei Amanohokosaka and other members of the Amanohokosaka clan, rendering her Drive inactive until she escaped. 
Ragna the Bloodedge gained this Drive when he began to use the Azure Grimoire. He used it inside the Embryo to take the dreams of the chosen, and eventually created a new world with the dreams that he had gathered.
As the name implies, Soul Eater devours the souls of those around it, using them to heal its wielder and strengthen their life-force. The strongest possessors can control Soul Eater, making sure to limit this aura solely to contact; kissing a victim can drain the life-force much more quickly. Soul Eater has difficulty regenerating wounds caused by Nox Nyctores weapons, especially those caused by Deus Machina: Nirvana because its claws were made from Kushinada's Lynchpin.
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