Soul

The Soul, along with the Body and Heart, is a part vital to the complete existence of any living thing. The soul literally give the body life, it is the difference between being alive or dead. It is the force that wills the body to live, and drives it to survive.

Part of a Nobody
When someone becomes a Heartless, their heart, the thing that controls the body, is released and they leave behind their body and their soul. Usually, the body and soul, having no guidence, wither away. However, if that person's heart was strong enough, then the soul will take command of the body and will it on. This being is called a Nobody.

Life and Death
Unlike the heart, with controls the body, telling it what to do and giving it feelings and emotion, the soul is the energy and life the body uses to carry out the heart's commands. Essentially, the Soul is life. Therefore, it is assumed that the soul is the spirit or ghost that leaves the body upon death. The body has no energy or drive to carry out the hearts orders, so ultimately the being dies.