Exagerration in animation could be physical or theatrical. Physical could be for instance drawing a human face with extremely huge eyes (Which you would never see in real life-in this case the eyes are stretched, so stretching and squashing could be combined together to give an exaggeration effect). Exaggeration could also be theatrical, like for instance the elephant and the mouse, the elephant is not scared of anything, the only thing that scares him, is a little tiny mouse (We often see that happen in cartoons, and this is theatrical exaggeration).
So exaggeration is used in animation to give a stronger look to animated options, to give stonger expressions, it could be to make something look more realistic, for instancein real life something might look boring and pale when while exaggerated in an animation, it looks way more exciting, more expressive. Exaggeration is often used to give a character a more powerful expression, an expression that communicates more to the viewers.
Exaggeration could aso be used to create one's own style.