The principle that a detail the story makes prominent has to pay off: if a loaded gun hangs on the wall in act one, it should go off before the end. Named for Anton Chekhov, who gave the advice in letters to other writers.
Chekhov put it more than once. In an 1889 letter he wrote that 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. A screenplay makes promises the same way: a close look at an object, a rule spoken aloud, a skill shown early. The reader files each one and waits for it to matter.
The principle cuts both ways. A detail you linger on that never returns is clutter dressed as foreshadowing, and readers notice the broken promise. A payoff that arrives without its plant is a convenience: the flare gun nobody saw, the language nobody knew she spoke. Plant and payoff is the working name for doing both halves on purpose.
It does not mean every object on the page must fire. Set dressing is fine; emphasis is the promise. A red herring is a gun meant to mislead, and it still owes the audience a payoff: the moment they learn why it was there. When a rewrite cuts a payoff, search the earlier pages for the plant it leaves behind.
Chekhov's gun is about payoff: a detail the story emphasizes has to matter later. A MacGuffin is about pursuit: an object characters chase, whose exact nature matters less than the chase. A MacGuffin becomes a Chekhov's gun when the thing finally does something once it is caught.
Foreshadowing hints at what is coming. Chekhov's gun is the obligation that follows from emphasis: once the story points at something, it owes the audience a use for it. A foreshadowing hint can be the plant; the payoff is what keeps the promise.
No, only what the page makes prominent. A kitchen holds a hundred objects. The one you describe up close, capitalize, or put in a character's hands is the one readers will remember and wait on.
Not always. In The Seagull, Konstantin shoots a gull in the second act, and the gunshot that ends the play is Konstantin shooting himself. In The Cherry Orchard, two characters carry loaded guns that never go off, a choice that fits a play about people who cannot bring themselves to act.