The fictional sport J.K. Rowling created for Hogwarts students is Quidditch.
Quidditch is played on flying broomsticks by two teams of seven players. Teams score by sending the Quaffle through one of three opposing hoops, while Beaters use Bludgers and the Seeker attempts to catch the Golden Snitch.
The Golden Snitch is worth 150 points and usually ends the match when caught, although catching it does not automatically guarantee victory. This scoring rule is one reason readers sometimes oversimplify the game as a contest decided entirely by the Seeker.
Rowling has said the name was inspired by the fictional game’s development in her notes and by the word “Quidditch,” rather than by an existing real-world sport. The sport appears throughout the novels and became a major part of the films’ visual identity.