Character Costumes offer:

The ability to change the Character’s outfit in the Main Game, including cut scenes.
Bonus Cash and time multipliers to certain Businesses.

Costumes can be earned in chest (when you complete a Season) and by competing in Events.

 

If your Characters have costumes available, you’ll see a little t-shirt icon in the Character screen:

 

You can change a Character’s costume at any time without worrying about which costume is better for profit because all costumes provide their bonus at all times even if they are not being worn.

As with Characters, costumes have an associated rarity (Common, Rare, or Epic) and you can upgrade costumes once you have enough Cards and Candy.

NOTES:

Upgrading a costume will not count towards an “Upgrade Characters” Goal.
Costumes do not affect events.