There are several ways to save your progress in the game, using Facebook/Google Play/Apple ID. You can see the options available to you in the game menu. Tap on the button in the top right-hand corner of the screen and press on the Save Progress button in the menu, after which a window will open with save options.
Saving your progress will help you to restore your progress in the future when you change your device or to synchronize your progress if you play on more than one device.
If you save your progress via Facebook, you are choosing a universal method with which you can always restore or transfer your progress to another device, irrespective of the operating system it uses.
Choose the synchronization service that suits you best and sign into your account directly from the game.