A literary element that, at first, seems to have no purpose but is later revealed to be important to the plot. This is commonly thought of as a parallel of foreshadowing, but it is more properly interpreted as "do not include any unnecessary elements in a story."
The return of Carmelita Spats in The Slippery Slope after her seemingly unnecessary appearance in The Austere Academy is an example of Chekhov's gun.
"One must not put a loaded rifle on the stage if no one is thinking of firing it." -Anton Chekhov