Signing in with your Google Account gives you access to cloud saving, achievements and leaderboards through Google Play game services.
If you experience a problem logging in or accessing Google Play game services, or if you see an "Unknown Error" message, please try the following:
1. Find the Google "Play Games" app and uninstall it.
2. Reinstall the Google Play games app.
3. Reboot your device
4. Restart the game and try to sign in again.
On older devices:
Find the Google Settings app in your app list, and open it
Click "Apps with Google+ Sign-in" at the top of the Google Settings app screen
Find the title of the game you're having trouble with in the list, and click it.
Click on "Activities visible via Google to"
Choose who you want to share game activity (such as high scores) with and hit OK.
Now open the game and try it again.
If neither of these solutions work, try rebooting your device, and if that STILL doesn't fix it, you may need to uninstall and reinstall the game. (NOTE: Uninstalling will erase your current save game progress!)