Coins are used to obtain boosters additional turns or additional lives in the game. To get more coins, press on the store button at the top of the screen:
Once you press this, the coin menu will pop up, allowing you to select the coin package you would like to purchase. Transactions are processed through your App Store, so the payment information you have entered on your device (or Facebook if playing on a web browser) will be processed directly on that account.
You can use your coins to purchase boosters before the start of a game, additional moves at the end of a lost level, and lanterns during a level, which can help you clear difficult levels.