Suppressors do not fully silence guns. They reduce the noise levels of a gunshot by about 30-35 dB, which is about the same as earplugs.
This reduction in noise levels is accomplished by trapping the expanding gas behind a series of baffles that slow the gas down and allow it to cool. This slows and reduces the sound of the muzzle blast. While a suppressor will reduce the noise level of a gunshot, it will not eliminate it.
In addition to reducing the noise level of a gunshot, suppressors can also help to reduce muzzle flash and felt recoil. This is because the suppressor traps some of the expanding gas that would otherwise be expelled from the muzzle of the gun. This trapped gas helps to counterbalance the force of the bullet as it exits the barrel, which reduces felt recoil.