Chekhov's gun
Also said as Plant and payoff, Setup and payoff, Foreshadowing
If something is made prominent early, it should matter later. It comes from Anton Chekhov's advice that a loaded rifle on stage has to go off.
A setup is what makes a payoff feel earned, and a payoff with no setup feels like cheating. In a game it is also a promise: players do go back to try the thing you showed them.
Say it
“If the rope in the finale saves them, show it in the first room and let the player try it there. Don't let it appear for the first time when they need it.”
Where you’ve seen it
BioShock has Atlas say "would you kindly" over and over from the first minutes, as ordinary politeness, and it means something else entirely when the game finally explains it.
Not to be confused with red herring
A Chekhov's gun pays off. A red herring is planted on purpose to mislead you. A gun you forgot about is neither, and is just a loose end.