Far as I know, it doesn't do anything. If you have referrals, it means that when someone applied to join, they filled your name in the box where it asks which member (if anyone) they were referred by.
The referral system is applied in some of the other communities Andy own. It works with a system called the "karma system" in which members get karma points when they do good things around the forum and lose points when they do bad things around the forum.