A Firearm Suppressor, also known as a Silencer, is a weapon accessory used to lower the decibels the sound of a gun makes, therefore it is "suppressing" gunfire. They are inserted through the muzzle of the gun. The suppressor is seen in three of the Die Hard films.
The silencer is seen twice in Die Hard, and they are accessories of Hans Gruber's group. Karl carries one with him as he and Theo break into Nakatomi via the front entrance. He uses it to take out the first guard at the lobby desk, then the other after throwing his hockey puck smoke bomb.
Hans Gruber can be seen with his silencer after taking Joe Takagi with him into an empty conference room and unscrews it from his Heckler & Koch P7M13 pistol in front of him.