How does a silencer work on a gun?

A silencer is more properly called a sound suppressor. Silencers do not make a firearm truly silent, they only reduce the noise.

The sound of a gunshot is composed of two things - the blast of hot gas exiting the muzzle at high speed and the crack of the bullet breaking the sound barrier. The silencer deals with the gas.

The inside of a a silencer is a lot like a car muffler. It's basically a large can with barriers called baffles. The gas bounces around these baffles and in the process expands and slows down so that it makes little to no noise as it exits.