There are several parts to the Damper System listed as follows from the bottom up:
The Pedal Lyre: Pedals, cushions, pedal lyre guide rods, lyre braces.
The Trapwork: Levers attached to the bottom of the piano that connect the pedals to their functions of sustain, sostenuto, action shift (soft pedal), and sometimes bass sustain.
The Backaction: A system of second-class levers that are lifted individually by their corresponding keystick or as a whole by the damper tray. These underlevers may contain tabs that can be lifted individually by the sostenuto blade which in turn allows the player to sustain selected notes with the sostenuto pedal while playing staccato on top manually.
The Guide Rails: Wooden rails fastened to the belly rail that guide the damper wires with felt bushings so that the dampers may be accurately centered over the strings, travel vertically, and suspend over the strings without wavering while the key is being depressed.
The Dampers: Damper wires, heads and felts. Connects to the underlever at the bottom of the wire and sits upon the string with a strip of felt that is glued onto a wooden block. The felts must be of the correct density, size and placement to prevent the string from sympathetically overinging, and to shut the sound down after the key has been released.