It is important for your head to stay at a consistent level, but not necessarily in a fixed position, throughout the golf swing.  When someone is told to `keep their head still,' one of the things that can happen is restriction of the shoulder turn on the backswing.

Another problem arises on the follow through. When your head is in a fixed position, the hip turn is also restricted, commonly resulting in a topped shot. 

Allow your head to slightly swivel toward the right on your takeaway, and on the downswing, keep your eye on the ball but allow your head to swivel back to the left a bit.