The motion-sensory feature is pretty interesting, as it acts as a natural extension of your body. In the past, you only used your hands and fingers to play games, but with this new function, you can use your whole arms to move or rotate the controller in any direction.
The name "Sixaxis" comes from the concept of "six degrees of freedom." There are two types of degrees; translational and rotational, and each type contains three degrees. The translational axes are up/down, forward/backward, and left/right, and the rotational axes are pitch, roll, and yaw. That adds up to six degrees, or axes, of freedom, hence the name.