Chests are awarded based on number of spins, as long as there's a free spot available in the chest tray on the right hand side. There are also Free Chests available in the Shop every 4 hours.
Awarded chests take time to unlock. Silver chests take 3 hours and gold chests take 8 hours. It's a good idea to start the unlock of the gold chests at night so they're ready to open the next morning!
Opening a chest will award you with coins and stickers. The coins are what you use to spin the slot machines. Stickers can be used to match onto quest cards in order to complete quests that give extra rewards such as coins, gems and more stickers.
Keep an eye out for rare chests such as platinum, emerald and diamond chests! They're very rate and take longer to unlock, but they contain the biggest rewards! These rare chests can also be be purchased directly in the shop.