Costumes are an alternate outfit for your characters that also provide bonus multipliers to their associated hangouts.
When worn, costumes will override the default appearance of your characters in your main game map and even in cutscenes. And don't worry: costume bonuses are always active even if they're not being worn, so you're free to pick your favorite ones and change them at any time!
You can spot characters with available costumes and costumes themselves by the T-shirt icon on their card frame. The number on this icon indicates how many costumes you've unlocked for that character.
Costumes are only awarded on event milestones, so keep an eye out for them!
You can upgrade costumes just like any other cards, provided you have enough resources. However, costumes are not the same as characters and so they will not count towards "Upgrade Characters" goals.
Please note that costumes are unavailable in events -- they will not provide their bonuses within the event and the characters will always wear the event's costume.