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 bodt is a medium for a person's heart and feelings to be expressed in the physical world.
Becoming a Nobody
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 empety 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 soulwith no heart is a being called a Nobody.
Connection with the Keyblade
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 aquiring 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 acess to Riku's Keyblade-wilding powers.