It's when you fuck in a staircase. What did you expect?
Of course, staircase fuck could also refer to:
Taking out an erect penis (or similar sexual device) and attempting to stick it into a staircase.
To exclaim the word "Fuck" while in a staircase.
To use the word "Fuck" in quick succession, with each repetition being spoken at a higher pitch.
To declare to oneself that from now on, you will only fuck another woman if she is hotter than the last one you fucked.
"I caught my apartment-neighbor staircase fucking when I decided to take the stairs instead of taking the elevator."
"Fuck."
"Fuck fuck fuck."
"Duuuuuude look at dat booty! You could see that thang all the way from China. Nigga you gotta tap dat ass!"
"Naw man, I've done betta. I've promised myself to only staircase fuck from now on."