"Chekhov's gun" is a literary concept that says that every single element of a story should contribute to the whole. Another way of saying this would be that everything that is introduced in a story needs to have a function. Chekhov's gun is named after the Russian physician, playwright, and author Anton Chekhov. Chekhov is quite well known for being a master of the short story format. For Chekhov, if something is not essential to the story, then it should not be included in the story. The term "Chekhov's gun" supposedly originated when he said the following quote:

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.

I believe that the best example of Chekhov's gun in Richard Connell's short story "The Most Dangerous Game" is the Death Swamp. A bit before Rainsford is forced to become the prey, Zaroff gives Rainsford some hints about how to supposedly stay alive for a bit longer. Zaroff specifically tells Rainsford to stay away from the Death Swamp and the quicksand.

I suggest, too, that you avoid the big swamp in the southeast corner of the island. We call it Death Swamp. There's quicksand there.

According to Chekhov's gun, there is absolutely no reason for the author to mention this place and that trap unless it is going to be significant soon after. Rainsford does end up in the Death Swamp, and he is nearly trapped by the quicksand; however, he is able to use that dangerous area to his advantage, and he builds a trap that ends up killing one of General Zaroff's prized hunting dogs.