Rubber bushings work by absorbing energy through the elastic deformation of rubber. When a wheel hits a pothole, the impact is transmitted from the tire to the suspension, then from the suspension to the control arm, and finally from the control arm to the chassis via the bushing.
If the bushing were rigid, the force would be transmitted directly, and you would feel the shape of each pothole inside the car. However, since the bushing is made of rubber, the rubber is compressed and deformed when the force is transmitted, converting a large portion of the impact energy into heat, thus reducing the force transmitted to the chassis. This process is similar to catching a thrown ball with your palm; by pulling your palm back slightly, the impact of the ball is absorbed by your arm and muscles. The rubber bushings are like countless hands pulling back on the chassis.
