(If you like, you can scroll down to the end of this article and watch a video related to this topic.)
A common problem in the press is that - instead of reaching forward with the hips and using the rebound this creates - a lifter will accidentally reach backwards with the shoulders. The two movements - reaching forward with the hips and reaching backward with the shoulders - look almost the same, but one makes for a stronger press while the other absolutely hinders the press.
Reaching forward with the hips helps us in two ways - first, that nice rebound out of the hips gives us a nice launch at the beginning of the movement, and second, it helps clear our face back out of the way of the bar (a natural countermovement). However, if you reach backward with your shoulders instead, you’ll still clear your head out of the way of the bar, but you won’t get any sort of launch or rebound from the hips, and indeed, it will actually make for a much harder and weaker press.