Three-headed dogs are very rare creatures. It is unknown if, like the Runespoor, each head serves a different purpose. Their great weakness is the inability to resist falling asleep to the sound of music.

Rubeus Hagrid once owned a three-headed dog named Fluffy, which he obtained from a Greek man he met at a pub. Fluffy served as one of the obstacles to the Philosopher's Stone in 1992.

In Greek mythology, "Cerberus" was a three-headed dog that guarded the gates to the underworld. In order to get past him, music would have to be played for him to fall asleep, as portrayed in the movie.

More Info: harrypotter.fandom.com