Brains are akin to "Experience Points" in that they are continuously accumulated yet never spent. You will Level-Up automatically as you earn Brains. PowerUps and unlocking Creatures are rewarded for leveling up. You can find the rewards by tapping the icon at the top left corner of the home screen then selecting "Boosts".
Brains are awarded for frequent app usage and sustaining good financial habits. Brain earning details are in the Currencies tab, found by tapping the Coin balance at the top right corner.