Heart

In the universe of Kingdom Hearts, a being is composed of three parts: a body, a soul and a heart. The heart gives a being emotion, feelings, light and darkness.

All hearts, have both light and darkness within them. The only exceptions are the Princesses of Heart, maideins whose hearts are made out of pure light. The light and darkness within a heart conflict and define a person, allowing them to exist.

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. This being separates from the body and soul to act on its own instinct. This primal instinct, drives the Heartless to seek out other hearts and consume them, turning them into Heartless. However, when a Heartless is destroyed by the Keyblade, 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 and will becomes a Heartless, then the body and soul left behind may begin to act with a will of its 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, of course, known as part of Organization XIII. Nobodies are considered "not to exist", because they do not posses light nor darkness, wich are located in the heart.

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
So far, the only known requeriments to wield a Keyblade have been a strong heart. The keyblade of the Realm of Light chose Riku as it's master, but since he gave into the darkness to pursue his goals, the Keyblade went to the next person with the strongest heart, Sora. King Mickey found the Keyblade of the Realm of Darkness and became it's master. Roxas was able to wield the Keyblade (even though he didn't have a heart) because he was Sora's nobody. Riku later found/created himself a Keyblade, speculated to be the keyblade of the Realm of In Between. Even Kairi, a Princess of Heart, was able to wield a Keyblade.

The connection between the Heart and the Keyblade is expected to be further explored in the series.