Internal Inertial Dampers
The internal inertial dampers create a field that removes the effects of massive acceleration and deceleration on the crew. Without this field accelerating under full thruster power would probably result in the crew being flattened against the rear bulkhead of the room they were in.
As a failsafe, the ship will not accelerate or decelerate more than 1 metres per second per second while the Internal Inertial Dampers are offline.
The Internal Inertial Dampers are not required for warp speed as the whole area of space within the warp bubble is being moved as one, therefore crew-members inside the ship will not experience g forces.
As they are such a vital part of the operation of the ship, these systems are usually spread throughout the ship and are very difficult to damage.
The Internal Inertial Dampening field can be variable throughout the ship (dependent on damage or assigned power). This would tie in with the gravitation system. Entire decks could be evacuated and de-powered in order to conserve energy.
Power Requirements
The Internal Inertial Dampers only require 1MW per 100 square metres per deck to operate, however this drain is constant when they are switched on (i.e. usually all of the time). They can be turned off to save power however this will restrict the thruster speed as mentioned above.