The high point of Mauresmo's backswing, shown here, is higher than most players use. This is a relatively large loop for a backhand. (A loop this size on a forehand would be considered small.) Having a loop on the backswing probably enhances the smoothness of Mauresmo's swing, but it's certainly not required in order to generate a smooth swing, and a loop can complicate timing and racquet position for some players. It's worth experimenting with your own backswing to see whether a loop helps or hurts.
Having her left hand on the throat of the racquet helps ensure Mauresmo's strong shoulder turn.
Mauresmo is using a modified Eastern backhand grip on this particular shot, but as we shall see, she varies her backhand grip quite a bit, much more than most players do.