A unicorn was one rare possible corporeal form of the Patronus Charm. Constance Pickering's Patronus took the form of a unicorn.

What does the unicorn Patronus mean?

According to Newt Scamander, the unicorn 'is a pure white, horned horse when fully grown'. They generally avoid human contact, so a unicorn Patronus might indicate shyness in a personality as well as an air of mystery.

Is there a unicorn in Harry Potter?

Unicorns are first introduced in Harry Potter and the Philosopher's Stone. When Harry, Hermione, Ron and Draco serve their detention with Hagrid in the Forbidden Forest, it is their task to find a wounded unicorn.