to wrap everything into one:
The Organization members (Unknown), call themselves Nobodies. They want to find out about the mysteries of the heart. Reason is they want to know how Sora was able to keep him memory as a heartless and return back to normal. What is unknown is the motives that the organization has. It appears as though the motives are good because Riku and Mickey join at the end of CoM. But we dont know for sure, we'll have to wait for Kingdom Hearts 2.