Heart

In the universe of Kingdom Hearts, the heart is a part vital to the complete existence of any living thing. Just as people have hearts, so do worlds. Any being of a certain quality will averagely have a heart, a Body, and a Soul.

Hearts apparently give the soul and body emotion and feelings, as well as a conscience. Nobodies, who lack hearts, cannot feel or show emotions.

All hearts, with a couple exceptions, have both light and darkness within them. Such exceptions include the Princesses of Heart, who lack darkness and have only light in their hearts. The light and darkness within a heart conflict and define a person, allowing them to exist. This is why nobodies are considered "not to exist"; not because they physically aren't existing, but because they lack the tool (the heart) that defines people and allows them to be.

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. This being seperates from the body and soul to act on its own instinct. This primal instinct that one could consider to be reprodutcion drives the Heartless to seek other hearts and consume them, making more Heartless. However, when Heartless are defeated properly, the darkness releases its grip, and the captive heart is freed. Eventually, these freed hearts congregate and collect together to make Kingdom Hearts.

If a person with a strong heart becomes a Heartless, then the body and soul left behind may act with a will of their own. This being is called a Nobody. If the person's heart was particularly strong, that Nobody may even retain its human form and memories, but will still lack true emotions which come from the heart. These specific nobodies are part of Organization XIII.

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 is therefore safe to assume that, since the members of Organization XIII can remember certain things (such as how to break a heart), then they must have either shadow hearts, which contain memory, or fractions of their old hearts.

Connection to the Keyblade
It is said that anyone with a powerful heart may wield a Keyblade, but if one forgets he/she ever wielded a keyblade, it is no longer possible to wield it. It should be noted that Roxas is capable of wielding Keyblades, but this is due to him being the Nobody of Sora and indirectly inheriting his ability to wield.