The word varsity identifies the starting team in a sport at a college or university. You have to be good to make varsity.
At many schools, sports are a big deal. Thousands of people flock to college football and basketball games, plus other sports. The members of the starting team are varsity players. Varsity players are the best players: that’s why they start, and they usually finish the game too. It can take a while for a player to make varsity status.