God42 has the basic gist of it but there is more.
A shell is basically the body, in the most simple sense of the term. So, the term "shell" is taken literally like a walnut shell or an egg shell or anyhting that surrounds something hidden; in this case the shell surrounds and protects the heart. Without the shell the heart becomes victim to anything that finds it. Ansem cast off his shell and actually had the ability to control his heart afterwards and plunge into the world of darkness. No one has any idea what happened to him in there. Whether he became victim to the heartless like many others or if he actually found the way to control them is anyone's guess. The organization members are actually just shells themselves. They have no heart and are seeking to find theri hearts again to become full beings so one could assume that the shell (or body) retains the mind but looses it's concience thought and all sense of right and wrong and simply wants to retrieve the heart, like it believes that to be it's only purpose. Then again, without a heart - without any emotions - who wouldn't try to regain it?
Basically, shell = body and heart = emotion and concience
