Update: according to this post by Punit Soni, the app is indeed exclusive to the Moto E for the time being. Other Motorola phones (Moto G, Moto X, and the Droids) will get access to Alert at some point.
My grandmother is 76 years old, and I've finally convinced her that taking her ancient RAZR V3 cell phone on the tractor when she mows the pasture is a good idea. Not because she actually uses it, but because the thought of her having to walk across 80 acres of snake-infested coastal when something goes wrong is a sobering one. Motorola knows the practical use of a cell phone in an emergency, and is augmenting it with a new app.
Motorola Alert does just one thing: tells other people where you are. Select the contacts you want to alert, and once you activate the app, it will periodically send your location to them. You can also set up specified points for unique alerts, for when you're leaving home or school, for example. It's hard to think of a situation where you'd be able to activate an app and want to do so instead of, you know, just calling 911, but I suppose this could help parents get a quick fix on their kid's location. The app's APK file is named "Bodyguard."
It looks like this app might be designed specifically for the shiny new Moto E. It's showing incompatible for just about every Android phone, including the Moto X and the 2013 Motorola DROIDs. It's also possible that someone published the app early and didn't remove the model restrictions, or that Motorola is trying it out in certain territories before a wide release. If you can install Motorola Alert, drop is a line in the comments with your device and location.