A motion compensator is a device that decreases the undesirable effects of the relative motion between two connected objects.
These negative effects include (1) the changes in force and stresses, and (2) the hysteresis, i.e., the rapid start-and-stop "jerking" of the objects.
Not only does the anchor prevent the ship from drifting, but the chain itself dampens the movement of the ship due to undulating motion of the waves.
Generally, motion compensators are implemented as springs.
For very large forces (dozens to hundreds of tonnes), the springs are implemented as gas springs: hydropneumatic devices — a plunger cylinder buffered by a volume of gas.