Do not read this if you don't want to know what Organization XIII is really doing. I can't remember if it has been revealed to you specifically at the point you are at in the game.

(SPOILER)Organization XIII is a group of powerful nobodies using Sora to destroy the Heartless with his keyblade. Every time he kills one, a captive heart is released and taken in by Kingdom Hearts. When they have enough they will become complete humans, gaining hearts, and abandoning the title of nobodies. Being nobodies, they cannot feel guilt or remorse and are not sorry for their ruining of the various worlds.