iOS 8 introduced the Health app, which I have covered a few months back about tracking your steps. Another feature customisable within the Health app is the Medical ID.
Medical ID allows you to display important information in case of emergency. This information can be accessed even while a device is locked.

After you swipe to unlock, tap Emergency.
On the emergency dial screen, tap Medical ID towards the bottom left corner.
This will then display the relevant information you have configured. You can set multiple emergency contacts who can be called even while the phone is locked.
To setup your Medical ID, launch the Health app and click on the Medical ID section. From here, click Edit and then add as much, or as little, information as you would like.
I hope emergency personnel such as paramedics and law enforcement have been made aware of this feature.