The anterior group is the muscle responsible for abduction, flexion, internal rotations as well as transverse flexion. Basically, when you raise things to the front or push objects forward these muscles go to work. In other words, as with the entire deltoid muscle, the primary function is to move the arm away from the body, specifically to the front.
The front shoulder muscle group is usually a secondary muscle group used for many exercises, especially those involved directly in the pectoralis region. Popular exercises such as shoulder presses or front raises are the most effective at toning and building this area.