The most important animation principle is called squash and stretch. When an object moves, its movement indicates the rigidity of the object. Many real world objects have little flexibility, such as furniture, however most organic objects have some level of flexibility in their shape.
Take for example a bouncing ball. A rubber ball bounces higher and squashes more upon impact than a hard league ball. The ease with which an object squashes and stretches defines the rigidity of the material making up an object.
When a person smiles, the shape of the face is determined by the movement of muscles underneath a layer of skin. During a smile, though the head seems to increase in size, with the widening of the mouth and jaw, it does not. The object is simply displacing its matter into the stretched shape. The most important rule to squash and stretch is that no matter how squashed or stretched out an object gets, its volume remains constant.