What exactly is backed up if I select app data in the sync options? Here, app data, what exactly is backed up if I check this option?   

If I uninstall an app, and re-install it, will its data (like my progress/score of a game app) restored?
AppData on an Android device is all data that is stored locally by an Application except for the binaries of the application. So your saves, progress should be backed up, but not the app itself. It usually depends on the Android operating system but it is generally what I said above.