Combat points (often abbreviated cp) are a type of points earned when defeating powerful opponents. They can be used to improve almost any skill or spell, though this is a time consuming process as any given skill takes a number of combat points to improve by only 1%. Note: You cannot improve multiple attacks using combat points.
This is the only way, however, to improve certain skills that do not have a chance to improve with use once you have practiced them to their limit. Combat points are generally used to improve skills that are extremely hard, costly or impractical to get better at through use.