Here is another student example (left hand clip) of the "waiter's tray" position. Watch how the strings of this player's racket face the sky as the arm extends upward. From this "waiter's tray" position, it becomes impposible to rotate the arm and racket into contact. And it is this torquing motion - this twisting of the entire arm and hand - into contact that leads to big serves.

The player on the right, Florent Serra, demonstrates the perfect "Big L" Position right before impact. His strings face the side fence in this final frame, and the edge of his racket runs parallel to the ground.