Trophies are what indicates your progress through the Training themes. You get a trophy for completing all the challenges in a theme, plus a Style Challenge in which you can style your outfit freely. In the Style Challenge, you’re not dressing up according to the tags – instead, you need to come up with your best look that other players are going to vote for when comparing it to other players’ looks.
If you get a sufficiently high score in the subtheme Style Challenge, you passed that theme and will earn a trophy! Now you can move on to the next theme!
Collecting all the trophies in a theme set will give you a diamond reward.