dawico is right on track there. The supressor will muffle the sound of the actual firing of the round inside the chamber and through the barrel, however you will still have all of the noise from the action cycling and, if the ammo is supersonic, you will hear the sonic report of the bullet as it travels through the air.
Take a .22 for example, the signature "crack" of a .22 LR is due mostly to the sonic report. Take that same .22 gun with a supressor and subsonic ammo, and you have quieted the gun to a modest level.
So yes, supressors do work, although their effectiveness is very dependant upon a few variables.... the firearm used, the caliber, the velocity of the round, and quality/maintenance on the supressor. But Hollywood silent is just that... Hollywood.