The shimmy damper slows down quick movements of the piston inside the cylinder. It does this by forcing fluid through a tiny hole in the piston whenever it moves. When serviced, it's filled with special fluid as per the manual.
The nose gear shimmy damper has a special mechanism to handle fluid expansion and contraction. A small piston inside the rod is sealed by an O-ring until the fluid pressure gets too high. Then, the piston moves, releasing excess fluid through a tiny hole. This prevents damage to the main seals.