press on something
to push or depress something, such as a button, catch, snap, etc. Press on this button if you require room service. Don't press on this because it rings a loud bell.
press on(ward)
to continue; to continue to try. Don't give up! Press onward! I have lots to do. I must press on.
press something (up)on someone
to urge or force something on someone; to try to get someone to accept something. (Upon is formal and less commonly used than on.) He always presses second helpings upon his guests. She pressed a gift on us that we could not refuse.
press (up)on someone or something
to put pressure on someone or something. (Upon is formal and less commonly used than on.) The crowd pressed upon the child, squeezing out all his breath. The load presses on your car's springs very heavily.