Heart
The heart is a part vital to the complete existence of any living thing. Just as people have hearts, so do worlds.
Hearts appearently give the soul and body emotion and feelings. Nobodies, who lack hearts, cannot feel or show emotions. All hearts have both light and darkness within them, except the Princesses of Heart and a few other, who lack darkness in thier hearts.
If an individual, be they good or evil, gives into the darkness of their heart, they will become a Heartless, a being of pure darkness who seek out other hearts. Usually, the body fades away. However, if the heart was strong, then the empty shell that is left behind will become a Nobody, and then seek to reunite with their hearts.
Memories are also tied with the heart. If a person's memory collapses, such as the Riku Replica, their heart will collapse as well, rendering their body into a lifeless doll.
It should be noted that the 'heart' is one of the three things that make up existence of a living being. The other two are the 'body' and the 'soul.'