I had to look this one up. From Wikipedia: "Chekhov's gun is the literary technique whereby an element is introduced early in the story, but whose significance does not become clear until later on. For example, a character may find a mysterious object that eventually becomes crucial to the plot, but at the time of finding the object, does not seem to be important."
You know, the way it's mentioned here, it makes Chekhov's gun sound like a trite, hackneyed formula. It's actually a rule of dramatic writing. You can't have someone pull a gun out of a drawer in Act 3 if you haven't alluded to the gun's presence already (and I would argue you can't just allude; the audience must be made aware there's a gun there)--and I say "you can't" not because you can't, but because the audience will feel cheated. Similarly, you don't place a gun somewhere on the set/in the story without intending to use it later, for similar reasons.