The phrase "button press" refers to the act of pushing a button, typically on a device or machine, to make it perform a specific function or command. Full definition
It's not difficult; getting a strike involves a single timed button press. (dreamandfriends.com)
The game has three difficulty modes, easy, normal and hard; depending on the mode picked, the speed and required amount of button presses increases as you advance. (miketendo64.com)
It's well designed so that the taps generally come in groups, rather than mixing in with button presses. (playstationlifestyle.net)