It is when a soul is split and stored in an object. That way, if the person is killed, he isn't really dead. Half of his soul (or 1/7 of the soul in Voldemort's case) is still intact. It can therefore, be released and strengthened (like he was trying to do in the Chamber of Secrets with Ginny. Notice how his form was getting stronger and clearer until the Diary was destroyed.) Then he can become human again. At least that is my understanding.
But how does he get out? I mean if all the other 6/7th of him is gone. DD went on and on about how V wanted to work alone and not be dependent on anyone.