Levitates and moves bodies
As though invisible strings were tied to Snape's wrists, neck and knees he was pulled into a standing position, head lolling unpleasantly, like a grotesque puppet. He hung a few inches above the ground, his limp feet dangling." — Remus Lupin's use on fellow Professor Severus Snape
is a Mobilicorpus spell which is used to levitate and move humans, and hence presumably other animals, given the etymology.
incantation comes from the Latin words mobilis (which means "movable") and corpus (a term meaning "body").
Behind the scenes
It is probable, given the similar etymologies (they share the word mobilis), that this charm and the Mobiliarbus Spell are variations of the same basic spell, modified for their purposes.
It is possible, given the lack of record toward the contrary, that the victim must be unconscious in order for the spell to be performed upon them.
This spell bears similarities (including the etymology and effects) of the Levicorpus Jinx.
Notes and references