The Level and Star Chests are one of the constant in-game challenges where you can always win coins and boosters. Both chests have progress meters that show you how close you are to unlocking the reward, and clicking on the chest will show you what you need to accomplish before the chest opens.
Level Chest
You will be able to open the Level Chest every 10 Levels.
Star
You will be able to open the Star Chest every 20 Stars.