To make your Character stronger, go to your Roster and click on the Character you'd like to power up, then press the level up” button. If you press and hold the button, the Character will continue to level up until you no longer has enough resources to do so. Each levelup is more expensive than the last, and is paid for with coins, XP, and goo.
When you upgrade your character to certain levels, you will also unlock new abilities for that character.
Another good way to make your characters stronger is to increase their rarity stars using the “Promote Characters” button in the Base. You can read more about Promotions in the “What is Character Promotion and how does it work?” FAQ.