A hitbox is an invisible, collision based structure that interacts with attacks. It is different from the model (the visible character and his colors that you see). The hitbox is meant to compensate for lag and movement. When a character is moving, his hitbox is usually farther from the model.
Note: Mounts and Pets do NOT effect a characters hitbox. Similarly, if an opponent can't see you, then they can't see your mount or pet.
The champions' damageable hitboxes (also known as a hurtbox) from smallest to largest are: