Nobodies are born when a heart is swallowed by darkness and becomes a Heartless. They are the remaining parts left behind by the heart: the body, giving a Nobody form, and the soul, giving the Nobody life. There are occassions that when Heartless are created, Nobodies come into being as well. These occurrences happen on an average of one of every forty souls that are consumed by darkness.
Because of their missing hearts, Nobodies lack emotion. Although, some humanoid Nobodies pretend to possess emotions, fooling others as well as themselves. On the other hand, Nobodies manage to keep their memories of their former lives, but unusual Nobodies lack memories of their former selves. Such memories are the reason why they can pretend to have emotions. However, even though Nobodies don't have emotions, they can think and plan (as opposed to the Heartless, which are mindless and simply act on instinct, with a few exceptions). (Kingdom Hearts II)
There was once an organization of very powerful Nobodies known as Organization XIII. They attempted to take over the various worlds of the multiverse but were defeated and vanquished before Voyager ever encountered the Nobody species. (Kingdom Hearts II)
USS Voyager (NCC-74656) would be the first Federation starship to encounter the Heartless and the Nobodies. In what would be known later as The Away Mission From Hell both the lost away team on the Delta Flyer and the USS Voyager would encounter an alarming number of Nobodies. (Star Trek: Voyager - Dark Realm)