On a kick serve, the racket meets the ball at high speed, with the ball literally sliding down on the racket strings for several inches before it leaves the racket. The strings themselves stretch for as much as an inch at the impact.
This is why there’s a ‘sleight-of-hand magic’ to the kick serve. The racket continues its path ‘beneath’ the ball, which at first has near-zero velocity; in slow motion, you can see that the racket head ‘moves ahead’ of the ball just immediately after impact. The server may get the feeling that he has caught the ball and is then ‘pulling the ball down’ as he continues with the serve’s follow through. (In fact, he has hit up on the ball, but with the racket on a circular path, which is why the follow-through is to the side, rather than forward.) The ball initially travels up and then arcs down because of gravity and spin.
All this happens because the body is sideways (not facing the net), and bent at the waist so that the swing path is left to right in relation to the body but ‘up and over’ in relation to an imaginary vertical line ending on the ground. The ‘up and over’ motion also reflects the ‘shoulder over shoulder’ rotation that creates the power for the serve.
References
From Popular Mechanics
https://www.popularmechanics.com/adventure/sports/a2072/4221210/]
Pancho Gonzalez’s serve on YouTube