This notifications log is cleared when you restart your phone. Android 4.3 is only available on the Nexus family of devices by Google — and a few custom ROMs have showed up bringing the unofficial Android 4.3 based on CyanogenMod 10.2 to a few devices. This feature looks not completed yet, but Google must have some use of it in the next coming up Android release.
NOTE: This app will only work on Android 4.3.