Stretch and Squash is hugely important in animation. The principle gives the weight and flexibility of a fixed volume. I allows more life to be projected into the piece, giving the various personalities portrayed through the actual make up of a character. It allows animators to distort a shape to show how various forces can act upon it.
Volume is a huge factor in that is considered with this principle. The shape stretches and squashes depending on how the force act on it, however the volumes of the shape must remain constant throughout.
I love this Disney references for Mickey, Minnie and Pluto. They show exactly how the principle works on the characters, before returning to the neutral pose.
This video showed the various frame by frame actions of a bouncy ball, showing were and when this principle comes into effect. The ball stretches as it falls through the air and the squashing as it strikes the ground.