Why does placing one hand on the head track stabilize you during turbulence?
He's just saying that you can brace your torso, and transfer the airplane's movements into your torso better so you don't sway around relative to the floor, by holding something rigid with your hand anchored at or just above shoulder level.
If you've ridden in a subway car that is rocking back and forth while standing up, holding on to a vertical post, you've probably noticed it's better to hold the post with your hand about level with your head, vs holding it down at your waist.  With your hand up high the car's motion is easy to transfer to your torso so you can stay more rigidly connected and you move as if you were part of the car.  Hold it down lower and you notice your torso tends to rock about the lower anchor point and your upper body sways more relative to the post, and this makes it a lot harder to stabilize yourself.