Nature
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. However, only those with strong wills such as Sora are actually able to continue on as Nobodies. Those with the strongest wills manage to retain human forms with some slight changes to their appearance, while the rest possess malformed, barely humanoid appearances. Therefore, the more humanoid a Nobody, the more powerful it is. This is opposite the nature of the Heartless, whose form is more monstrous the stronger the original heart is (with the exception of Xehanort's Heartless, who retained human form because he gave into the darkness willingly).
All Nobodies, vanishing from the realm of light upon the loss of the heart, are born in a world in-between the realms of light and darkness, like Twilight Town or Castle Oblivion. However, because of this and their lack of hearts, they are shunned by both light and darkness, and do not truly exist.
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), and possess memories of their past lives despite their lack of hearts. Nobodies also seem to be able to experience physical sensations, such as pain, as they negatively react to taking damage, and Naminé passed out from the pain of being impaled on Marluxia's thorns (this was seen only in the Chain of Memories manga).
Although never stated, the events of the Battle of 1000 Heartless implied that Nobodies are stronger than Heartless, since the Nobodies were able to easily overpower the Heartless. At the very least they are just as powerful, and the fact that they are much more intelligent than Heartless only heightens the threat they pose.
However, it seems that unusual Nobodies (like Roxas and Naminé) possess true emotions. This may be because they co-existed with their original selves (the Keyblade Master of the Realm of Light and a Princess of Heart, respectively) and held half of their essence within them, thus making them more human than other Nobodies.
