The short version is a suppressor coverts the energy that would be/is audible sound to heat and in some cases ultrasonic sound. The pressure pulse leaving the muzzle is spread out over time, thus lowering the peak sound level.
Let take a balloon for example. If you pop it, it's LOUD!!! But what happens when you untie it and release air slowly?? That's what the baffles do. The explosion slowly drives itself into each baffle area, lessening the force of the shot coming out of the end of the can. That's my description!