You earn Brains and grow your "Brain bank" by completing different actions within Long Game, such as logging in daily, depositing into your Savings Jars, hittings Savings Streaks, referring friends, and more. As you earn Brains, you level up and unlock more PowerUps, Creatures, and Games. You can find the rewards by tapping the icon at the top left corner of the home screen then selecting "PowerUps".
Brains are awarded for frequent app usage and sustaining good financial habits, and you never spend or lose Brains. Brain earning details are in the Currencies tab, found by tapping the Coin balance at the top right corner.