Idealy it controls yaw. In straight and level flight, moving the nose left or right. (if knife edge that's gonna be up down) However many planes have roll coupling with the rudder (more or less any trainer). This causes the rudder to also roll the wings. The rudder is among the last control surfaces to loose authority at slow speed, so it is important at slow speed. Aswell, at slow speed, ailerons could stall a wing and cause a tip stall. The rudder will be less likely to do so. However... no always. A snap roll for instance is often initiated with elevator and rudder. As you might be gathering, there's not a perfect anwser.
2 sites I very quickly pulled up on google with a search for flight dynamics
http://en.wikipedia.org/wiki/Flight_dynamics
http://www.ueet.nasa.gov/StudentSite...sofflight.html
Both are very basic but it's a good point to jump off from.
-John