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. A few might argue that the heart also departs with the soul.
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.' It is speculated that the soul is the reason for a Nobody's human appearance, though others are seen to argue this point, claiming it is the 'heart'.
