To go into detail about the construction would not be wise b/c then people like you and I would be building our own.
But basically is slowly bleeds off the gasses escaping the muzzle so the sound it deadened. I believe some also have a type of "insulation" inside to help.
My AWC Nexus - for the 1911 .45 - has a coil spring in the housing that screws onto the barrel, and it's twist lockable to either allow or restrict the .45 action cycling.
I haven't tried to figure it out, but I reckon one mode allows the barrel to slide backward during recoil (compressing the coil spring?), thereby unlocking the action, reloading the chamber and recocking the hammer - allowing the recycling process to complete, though somewhat slower than normal due to the suppressor's weight slowing the process. And the other mode "locks" the action in place, making for a quieter overall effect.
'Course, that's probably bass ackwards from what's actually taking place engineering-wise - but it sure works sweet