When you think of voice mail, it's not something that would excite you or would make you think of high-tech visual apps. All you would want is something that is practical and something that works. That is probably what Motorola was thinking when they created the Visual Voice Mail, which is not the most exciting app around, but gets (or should) the job done.
The Visual Voice Mail just has one function, and that is to make it easier for you to access your voice mail without having to dial through your phone. You will be able to access them through the app directly, which will be included in your carrier plan. It will show you a list of voice mail messages (both read and unread). You can delete those that are useless already and manage them directly on the app without having to go through the usual voice instructions on your phone.
The app is truly basic and does not have any kind of design or feature that should enhance the experience of using and managing your voice mails. And it also does not work with all of the Motorola X devices (particularly the 2013 and 2014). But this may probably be due to the fact that this might be a Verizon-only app as seen on one of the screen shots on the app page.
So if you're on Verizon, you can download the Visual Voice Mail app for free from the Google Play Store. No in-app purchases necessary, although of course, you need to be under a carrier plan to be able to use and access your voice mail.