Google’s new solution for device owners to track their lost or misplaced smartphones has started showing up on some Android phones. The application seems to be a part of Google Play Services app, which will automatically get updated on your device.
As the web version of the service is not yet live, Device Manager is of no use right now, however if you still want to get Android Device Manager, you can download the latest version of Google Play Services from here (or here) and install it on your smartphone (usual disclaimers apply).
Some reports indicate that there are going to be multiple Play Services app versions for different screen-densities, so it is better if you wait for the official roll-out or uninstall the updated version once the official release is available for everyone.
You can also check in settings << security << device administrators, if Android Device Manager has automatically reached your smartphone or not.
To remind you, Android Device Manager allows users to track their smartphone location in real-time, ring their phones and even wipe all personal data.