Campaign is a game mode in which you play teams of increasing difficulty with larger rewards as you go on, unlocking new opponents as you beat the others. Playing campaign opponents requires tickets, which regenerate over time.
To start with, you can only play teams which require four tickets to play. You earn one star for beating an opponent once, two stars for beating that team by five goals (30 points) and three stars for beating it by ten goals (60 points).
The two benefits of earning stars are unlocking new opponents with greater rewards, and unlocking the ability to Walkover, where you can spend tickets and earn rewards as if you had beaten the opponent without needing to play the match. Earning two stars gives you the ability to Walkover once, and three stars means you can Walkover multiple times.