The soul (魂, tamashii?), along with the body and heart, is a part vital to the complete existence of any living thing. The soul literally gives the body life, and is the difference between being alive or dead. It is the force that wills the body to live, and drives it to survive.
When someone becomes a Heartless, their heart, which controls the body, is released and the body and soul is left behind. Usually, the body and soul, having no guidance, wither away. However, if that person's will was strong enough, the soul will take command of the body and will it on. This being is called a Nobody. Exceptionally strong Nobodies, such as the members of Organization XIII, retain their human form. Therefore, it is clear that will is related and is an essential part of the soul.
Unlike the heart, which 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. If the soul leaves the body, it has no energy or drive to carry out the heart's orders, which ultimately causes the being to die.