When quadcopter is flying, in order to to maintain balance either automatically or manually, the motors changes speed to adjust roll/pitch/yaw angles. Therefore even with the best balanced aircraft, you will still see some level of shakiness in your video. By using a camera gimbal, it compensates the change of roll/pitch angle, and leaves the camera steady so you have perfect images.

Camera gimbals can remove some of the shakiness by stabilizing all three axes (Pan, Tilt, and Roll or sometimes just 2 axis) with the help of brushless motors or servos, and sophisticated sensors and micro controllers. You can freely move around with your camera and the Gimbal will keep it steady.