The soul is a part vital to the complete existence of any living thing.
Souls literally give the body life, as in being alive and not dead.
When someone becomes a Heartless, they leave behind their body and their soul. Usually, the body/soul fades away. However, if the heart was strong, then the remaining body and soul will begin to move and act on its own, becoming a Nobody with the soul giving the Nobody life.
When someone naturally dies, it is assumed that it is the heart and body without the soul, which renders them lifeless.
It should be noted that the 'soul' is one of the three things that make up existence of a living being. The other two are the 'heart' and the 'body.'
