Body
The Body, along with the Heart and Soul, 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 a 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, and their heart is released, they leave behind their body and soul, which is an empty shell and usually withers away. However, if that person's heart was strong enough, the soul will take control of the body and the shell will start to act on it's own. A body being controlled by a soul with no heart is a being called a Nobody.
While the Heart is the deciding factor as to if a person can wield the Keyblade, the body can be used in a loophole for acquiring the Keyblade, as seen with Xehanort's Heartless and Riku in Kingdom Hearts. Xehanort's Heartless possessed Riku's body, therefore bypassing the heart and giving Xehanort's Heartless access to Riku's Keyblade-wielding powers. Sora who can wield the Keyblade released his own heart and Roxas became apart of the Organization as "The Keyblade Wielder". Being Sora's Nobody, Roxas could wield the Keyblade.
But, since Kairi saved Sora by using her power to give his heart back, shouldn't Roxas have gone back to being Sora's body? Or maybe Roxas took Ventus' body?
Organization XIII wanted nothing more than a Heart to be complete and have emotion. Every Nobody wants to exsist and be chosen by Light and Darkness as Xemnas said at the Castle That Never Was.