Leg Drive in the Bench Press
Executed properly, use of the legs creates stability and supports your arch. To do this, you endeavor to drive your body up the bench (in the direction of your head). You don’t slide in that direction, of course, because the bar is pinning your shoulders down to the bench, but the act of attempting to drive your body up the bench gives increased lateral stability (since you’re utilizing a roughly squat-width stance), a supported arch, and a certain amount of compression and therefore rigidity in your torso.
When people lift their butt up off of the bench, however, they are accidentally using their legs to drive their bodies vertically upward instead of horizontally “up the bench.”