The body (肉体, nikutai?) is a recurring factor and philosophy in the Kingdom Hearts series; along with the heart and soul, it is a part vital to the complete existence of any living thing. The body gives the heart and soul a vessel, granting a person a physical appearance and form. The body is a medium for a person's heart and feelings to be expressed in the physical world.
The heart controls the body, much like the brain in the real world, so when someone becomes a Heartless or otherwise loses their heart, their body and soul usually wither away to nil. However, if that person's heart is strong enough, their soul will take control of the now empty body, which will start to act on its own, becoming a being called a "Nobody."
While the heart is the deciding factor as to whether or not a person can wield the Keyblade, the body can be used in a loophole for acquiring the Keyblade, as seen with Ansem, Seeker of Darkness and Riku in Kingdom Hearts. Ansem possesses Riku's body, thereby controlling his heart and giving him access to Riku's Keyblade-wielding powers.
Should a Keyblade wielder discard their body to transfer their heart into a new vessel, it vanishes from existence. It will return after the destruction of the Heartless and Nobody that comes from the vessel, as is the case for Xehanort, who was not able to absorb Terra's heart into his own. Through unknown means, Luxu can completely dominate his new host, making the body his own permanently.