Chekhov's gun is a dramatic principle that every memorable element in a fictional story must be necessary and irreplaceable, and any that are not should be removed.
Remove everything that has no relevance to the story. If you say in the first chapter that there is a rifle hanging on the wall, in the second or third chapter it absolutely must go off. If it's not going to be fired, it shouldn't be hanging there.
Variations on the statement include:
"One must never place a loaded rifle on the stage if it isn't going to go off. It's wrong to make promises you don't mean to keep." Chekhov, letter to Aleksandr Semenovich Lazarev (pseudonym of A. S. Gruzinsky), 1 November 1889. Here the "gun" is a monologue that Chekhov deemed superfluous and unrelated to the rest of the play.
"If in the first act you have hung a pistol on the wall, then in the following one it should be fired. Otherwise don't put it there." From Gurlyand's Reminiscences of A. P. Chekhov, in Teatr i iskusstvo 1904, No. 28, 11 July, p. 521.
