Dwight: Most "cushion underframes" have all or part of the center sill, with the draft gear, able to slide. It's attached to the rest of the underframe with either springs or hydraulic "shock absorbers", in principle not unlike the suspension on an auto. When the car is coupled to, or moved abruptly, instead of the draft gear transmitting the shock directly to the car, and load, the center sill moves, and the cushioning system absorbs the shock. It is then transmitted to the rest of the car gradually, reducing the chance of load damage.
Since the couplers have to be able to move relative to the car, they stick out further than usual, to allow them to move in without the two cars hitting each other.