The wrist motion of the thumbs going up and down is am important part of the swing to understand. Clearly just a few degrees of motion in the wrists have a big impact on shaft position and face angle.
In most of the swings we see in lessons, people generally don't have enough of the thumbs down position through impact. Having the thumbs down goes hand in hand with a flat or slightly bowed lead wrist and an extended trail wrist. Those are the positions that you want to see in your swing at impact. When you have the trail thumb down with wrist extension it keeps you from flipping the club and you get much better compression on the ball.
So check out what you can learn from coach Nathan Ouimette in this video in terms of where the thumbs should be at setup, at the top of the swing, and coming into impact. In particular note how the angle of the right hand at the full release point is basically the same as the angle of the hand at the setup position.