A quick definition of sports franchise:

A sports franchise is a special permission given by a professional sports league to a person or group to create and manage a team in that league. It's like being given a special key to start a new team and play against other teams in the league. The team itself is also called a sports franchise. It's like having a special toy that only you can play with, but instead of a toy, it's a whole team that you get to control and manage.