Head position during the swing is an element of the golf swing that gets overlooked by amateurs and professionals alike. I feel that having a still head during the swing contributes to hitting the golf ball with power and consistency.
The reason why I feel that keeping a still head helps generate consistent contact is because it keeps all body parts in the correct position to make a descending blow on the golf ball. Hitting down on the golf ball is the key to consistent contact and an ideal trajectory, especially with irons and wedges. You want to hit down on the golf ball with all clubs except the putter and the driver. With those clubs you want to actually catch the ball slightly on the upswing.
During the backswing, I like to see my students keep their head as still as possible and rotate their upper body around their spine. This creates a torque, which is the upper body twisting against a less active lower body. It is important to keep your spine angle consistent and not alter your posture during the backswing. In video analysis of the swing I like to draw a circle around the head and a line down the spine to see if there are any changes during the backswing. This helps identify problems because watching with the naked eye can make it difficult to spot changes in the positions of those parts. I would say, however, that many great players have moved off the ball slightly with their heads during the backswing. If you are going to move your head at all you want to move it away from the target just slightly. Only a matter of millimeters or inches is acceptable. It is when you move your head back away from the target a few inches or more that you encounter problems with ball striking. Moving your head off the ball too far will lead to inconsistent contact with the ball.
The problems that arise with moving your head too far backwards during the backswing all relate to contact. Many thin and fat shots come from making this move. The reason is that when you move you head back you move your entire body and the center of your swing back. In order to hit the ball, you need to move everything forward to compensate for that backwards move you made during the backswing. If you don’t move forward exactly the same amount you moved back, you have changed the center of your swing. This makes it impossible to hit the ball correctly unless you throw your hands at the ball, which leads to even more problems down the road.
During a proper transition to the downswing, I like to see the head remain still as the upper body uncoils and delivers the club to the ball. Right at impact, the spine will bend a little bit, which may force the head to move down toward the ground some, which is fine. After impact, you can move your head slightly toward the target and lift your head up a bit to see where the ball is going. It is important, thought, to keep your spine angle consistent until after the ball is struck. Many people tend to stand up and lose their posture near impact, which can lead to errant shots.
I hope this idea of keeping your head stationary during the swing helps you to make better contact with the ball and results in better shots.