The right arm's role in the backswing is under-rated and often misunderstood. In fact, many amateurs do the opposite of what they should do.
Simply put: The right arm should be on top of the left arm (1) as you start the backswing, and then it should move under the left arm (2) as you swing the club to the top.
Many amateurs fold and shorten the right arm too early as they snatch the club away. You really want a relatively straight right arm during the initial backswing as this promotes width and good pace - keys to hitting solid shots.
As your right arm continues towards the top of the backswing, it should start to fold and move under your left, which encourages your wrists to set and load correctly and helps your upper body make a full coil. This combination sets you in the ideal position for the downswing.
So, with the right arm, think "on top then under" as you swing back, for a great start to the golf swing.