Usually it's used as an imperative - 'Drop and give me twenty/fifty/a hundred!'
It's a set phrase that comes from the military. Typically, it's said by some officer, often a drill sergeant, as corporal punishment for some offense by a low-ranking recruit. It would be particularly common during basic training. You might also hear it from a physical trainer.
'Drop' refers to the fact that you have to drop down flat on your stomach to begin the push-ups.