Good ball strikers create a wide arc on the backswing because they accomplish a couple of things:

as they swing back, they naturally hinge their wrists, which puts the club on the proper plane and
they are flexible enough to make a full turn while maintaining the lead arm extended.
High-handicappers tend to do the opposite: first, because of a faulty grip they are unable to hinge their wrists properly and then usually end up hinging their elbows instead and second, because they may not be as flexible, they are unable to make a full turn and keep the left arm extended which makes the left arm bend at the top of the swing.

Here's a drill to help you stop bending your arm at the top.