In order to save your character and not to lose your game progress, you need to synchronize your game account with Google Play/Game Center (depending on your device).
This can be done in the game settings:

1. Tap the "Settings" button in the upper right corner.
2. Select the "Profile" tab.
3. If it says that you are "Not signed in", tap the "Connect" button.
4. Once everything is ready, the text will turn into "Signed in".

Also, you can find your character's numeric ID in the "Settings" tab. If you lose your game character, it can be restored using this ID.