A soul eater is a supernatural entity that resides in The Realm. It has no face and preys on a living person's consciousness. If a living person's consciousness travels to the Realm and is absorbed by a soul eater, they are not able to return to their body.
Soul eaters are shapeshifters, and take the shape of the person/thing that is most likely to work on the victim. In Frost's case, the soul eater took the shape of Celeste in order to lure him into being killed by the soul eater. In Holden's case, it attempted to kill him by taking the shape of a wolf and attacking him.
Soul eaters live on the side of The Bridge where death resides. Their main goal is to cross over, and when Holden built the bridge between the Living and the Dead, the Soul Eaters crossed over and destroyed The Realm. Furthermore, according to Holden's dream, their next goal is to attack the real world.