Mini events are a short timed event that requires you to obtain a specific set of items in exchange for a prize.
The exact time limit before it ends can vary and sometimes more than one can occur after the previous one ends.
When a mini event is occurring, you will see a new icon near the bottom of your screen that can be tapped, allowing you to see what is required in order to redeem the prize. The prizes can vary from currency to characters or other wonderful decorations. So be sure to take a look and participate!