Most importantly, the outfit drives which charge attack and skills animations the character uses in battle. All other options are based on the character's current outfit. To avoid confusion with the character's other variants, Inventory, Character Details, and Star Character settings won't be affected by choosing an outfit different from the original. It affects most of the settings below as far as what options you can choose.
The character's outfit dictates the art and sprites that you would like to use for this character.