AT&T has started pushing out a software update for the iPhone 5 and the iPhone 4S in the US, which adds support for Wireless Emergency Alerts.
Once you install this update, your phone will be able to receive these alerts, which are issued by the government. You will receive notifications for things such as AMBER (America's Missing: Broadcasting Emergency Response) alerts, emergency alerts for man-made or natural disasters or Presidential alerts.
After installing the update, you will find two new options in your Notifications settings menu on your iPhone. Here you can choose to disable the AMBER alters and emergency alerts but the Presidential alerts will always be on.
The update is being pushed out by AT&T and should be available on your iPhone 5 and 4S by now.