Power up events are multi-day events where you can activate a power up for certain heroes, giving them greater combat skills (Max HP, Skill Power, and Basic Damage) in all aspects of the game where you are the attacker. This bonus does not apply to your defense teams.
Use your power ups wisely! You get a limited amount of time each day to use the power up. Once the time runs out, you need to wait until the next day to activate it again. The power up chance resets with your daily resets at 5AM.