After pulling the butt cap forward briefly through the slot, with the wrist twisted back and down, it's time to generate racket head speed. By quickly rotating the butt cap with the hands, the racket will travel "inside out" in a burst of speed. This inside out burst is identical to what happens on the forehand and "the fan", but here it's created by two hands quickly rotating the racket around the butt cap of the racket.
This burst of racket head speed will turn into a powerful drive of the ball as Andy uses his left arm as a lever. Watch how the left arm functions as a lever to meet the ball as the hands and racket head whip around. And then the left arm lever powerfully lifts upward and across the body for power and extension.
In the final frame notice how Andy's chin is touching that powerful left shoulder muscle. He started the stroke with his chin over his right shoulder. And he finishes with his chin over his left shoulder. By finishing with his chin over his left shoulder, he guarantees that the entire arm (acting as a lever) has driven the ball from the shoulder.
Also notice how his arm ends up across his body in the final frame. Because the left arm functions as a lever, its full range of motion is to lift upward and across the body.
The magic of this shot comes from combing the burst of racket speed from the hand rotation into the powerful drive from the left arm as lever. Speed from the rapid rotation of the hands combined with power and drive from the arm and shoulder create the professional two handed backhand.