Settings > Backup and Reset > Google Account.
Select the Google Account where you want to back up your data.
Make sure 'Backup My Data' is turned on - (with a green or colored button).
Once this step is checked to go back to:
Accounts > Select the Google account where you want to back up your data > Make sure all items are turned on with a green or colored button > Go to the top right of the page press on the menu/more button and 'Sync Now'