Most Characters are associated with a specific Business, and will increase the Business's speed, profit or F**k Off Power when you upgrade them. Ricky, Julian, and Bubbles on the other hand affect ALL BUSINESSES when they are upgraded! You can check out more info on how multipliers work here.
Check out the associated Business by tapping on the Character. For example, J-Roc supports Roc Vodka:
And Tyrone supports Mystic Fingers:
Check out our full list of Characters here.