Chests are rewards you'll receive for winning crowns and making progress in the game. There are several types of chests: you'll be able to find some of them in the main screen and a very special one in the "Events" section.
In order to obtain the chests displayed in the main screen, you'll need to get crowns in the different game modes. As you do this, you'll notice a bar that will start to fill until you reach the total number of crowns needed to open the chest.
If you want to obtain the "Events" chest, you'll need to complete the different events in that section in order to unlock it. Bear in mind that this chest will be available every twenty-four hours.
Once you open any of these chests, you'll receive gold bars, PowerUps and pieces for the thematic wheels.