I still remember years ago when I first started to play golf, the tip you heard the most was "keep your head still". My father used to say it to me at least 50 times a round. He thought he was doing me a favor,when really, he should have been telling me to do the exact opposite. He should have been saying "move your head a little on the way back".
Why move your head as you take the club back? You want to move your head because in order to swing in a circular motion you need an axis to swing around. An axis has a top and a bottom. When you set up to the golf ball, you have 1 top to an axis (your head) and 2 bottoms (your legs and feet) to an axis. This means that on the way back your head should be moving 3 - 5 inches to the right in order to create your first axis to swing around. Your head will stay there as you come down and fall even further back through impact. Then, after the ball has been hit, your head will move forward over top of the left leg to create a second axis. This second axis will allow you to complete the circular rotation in your golf swing allowing you to finish your swing. So what you have is a floating top to an axis. Your head floats back and forth to create 2 axis when you swing. This allows you to swing in a circular motion. It's not a perfect circle though. It's a slight oval. Because your swing is a slight oval, you will never hit the ball 100% perfect.
The only time you would keep your head still is if you had one leg. If you had one leg, you would have 1 top and 1 bottom to an axis. This means that if you moved your head you would destroy this axis. So maybe we should all be playing standing on one leg and keeping our head still? Unfortunately, this will never work because you will not generate enough power and you will probably fall over. Most people have enough trouble keeping their balance with 2 legs never mind 1 so it's best that you keep both legs on the ground and learn to move your head.
Most people I teach try to move their head back when I tell them to but they have a hard time actually doing it because it feels so uncomfortable for them to move their head. To get the proper feeling, you must feel like your head is moving about 1 foot to the right. If you feel like your head is moving 1 foot to the right on the way back, it will actually only move a few inches. Try swinging regularly towards a mirror. As you watch yourself swing, you can clearly see if your head is moving back 3-5 inches. As your head moves back, feel how your weight loads into the right leg. This is the tell tale sign that you have created your first axis in the backswing. If you don't have a loaded, powerful feeling in your right leg, you will have to move your head a little more as you go back. If you are wearing a hat when you play golf just take your backswing and look to see if the brim of the hat is level to the ground not tilted to the left. If the brim of the hat is level to the ground at the top of your backswing your head will have moved the proper amount. As a final check just ask a friend to watch your head to see if it moves back a few inches or use a video camera to see for yourself. If your head is too still then constantly remind yourself to move it back or have someone constantly remind you to "move your head".
As you move your head back, beware that it may cause you to hit behind the ball a little. This is a good sign at first. It's telling you that you are moving your head back but you have too much weight on your right foot at impact. To remedy hitting behind the ball (fat shots), all you have to do is feel a little more weight shift off of your right foot through impact. If you do, you will hit the ball perfectly and with much more power than you are used to.