Most of the power from a pitchers delivery comes from the legs and torso. Having the body pushing forcefully towards the plate, along with with the arm action increases the velocity on the ball. The leg that the pitcher pushes off on is the most important, as it is used to drive the body towards the plate. When the pitcher lifts up his front leg, he recoils the energy in his body, and then as her throws the ball, he drops and drives the energy towards the plate.
An example of how important a pitchers legs are is the Curt Schilling bloody sock game in the 2004 ALCS. In Game One, with his messed up ankle, he was unable to push off the rubber of the pitching mound, and drive the ball towards the plate. In that game, his fastball only reached the mid eighties. In Game 6, when he had his ankle temporarily repaired, he was able to push off the rubber, and his fastball was back in its customary 92-95 range.
Granted, I have never been a pitcher. But I still throw with people, and we pitch with a little velocity once and a while, and I have been trying lately to refine a pitching delivery, so if I ever play again in some sort of recreational league, I will be ready.