During the golf swing, there are very few fixed points of reference as the motion requires the movements of multiple body parts with hardly any staying still, the head, however, is a different matter.
Most of the greatest players throughout history have always kept their heads very still throughout the back swing and impact. This allows the swing to flow around a fixed point and stops any large amount of lateral movement back or through the ball.
During the wedge and iron swing where golfers need to strike down and through the ball, the head should be level with or slightly behind the ball during the back swing and down swing. As the club fires through impact, the head should be allowed to follow the natural body motion forward after the ball is struck. If the head was to hang too far back on a wedge or iron shot, there is chance of thinning or fatting the ball as the club arc will bottom out too soon. If the head moves forward of the ball at impact, bad strikes and a steeper angle of attack will be created. Keeping the head in a fixed position level or just behind the ball is a more consistent option. There are exceptions to this rule such as Lee Trevino whose head moved down and forward during impact. However, players like Trevino have highly individual swings, are the exception to the rule and should not be copied.
During the driver swing, it is even more essential to keep a nice stable head position. Because the driver has so little loft and the club shaft is so long it becomes even more important to keep the head slightly behind the ball at impact. The driver is different than the irons because the club arc bottoms out at a much shallower point (just above the ground) and for optimum drives, the ball should be struck slightly on the up. This is why the ball position for a driver is forward of center in the stance, just inside the left heel (for right handed golfers). This ball position allows the player to catch the ball slightly on an upward arc, sweeping the ball into the sky. If the head was to move forward of the ball at impact, the club arc would move forward, possibly causing the driver to strike down instead of up. Because of the already low amount of loft on the driver, a downward strike could cause an extremely low ball flight.
Although players can allow the head to move forward of the impact zone, after the ball has been struck every effort should be made to keep it level or slightly behind the ball when the ball is struck.