Star Points are a type of currency that you can see at the top right of the screen:
Star Points Konto
This new type of currency can be used to get exclusive items from the in-app shop (mainly character customizations) and can be earned by participating in the Trophy League. In other words, increasing the number of your character’s personal trophies earns you Star Points… but not always. In some cases yes, but in other cases you just earn normal Brawl Tokens. Anyway, to find out how many Star Points you get and at what trophy level, select a brawler and click on his personal trophy account:
Character’s goals for the Trophy League
Whether or not you can get these kinds of points is rather random as it depends on how many trophies a brawler has won. The reward for achieving certain goals is completely variable. At least now you know where to look it up.
That wasn’t the case before, there was the Star Tokens. These were special coins earned by winning matches in Brawl Stars. Once you had ten, you could exchange them for a Big Box. However, these have disappeared with the last major update and the reward system is now much more based on Clash Royale.
One more important thing: did you play Brawl Stars before the last major update? Did you win tickets for the weekend’s events? If If the answer is yes then Supercell has probably already notified you about the game itself as those tickets are now Star Points.