In Harry Potter, the form a Patronus takes represents something about the witch or wizard who cast the spell.
Harry Potter's stag Patronus represents his bond with his parents and demonstrates his leadership and courage, while Severus Snape's doe Patronus shows his love for Lily Potter.
Due to the connection between a Patronus' form and the person who casts the spell, Partonuses reveal much about the characters, demonstrating their personality, the people they love, or how they have changed over time.