Since March of 2010, Verizon has been including a Verizon Apps store on its Android and BlackBerry handsets. When it was first created, the app landscape on Android wasn't the same as it is today. Nowadays, we're not sure who actually chooses to get an app from the Verizon store rather than Google Play. Verizon realizes this, and is going to start completely removing its Verizon Apps store from all devices starting January 2013 via software updates. Beginning immediately, customers that have installed apps from Verizon Apps are going to be notified of the changes, and monthly recurring subscriptions will be set to expire in December.
The removal process is expected to be completed by March 2013, but Verizon points out that certain apps -- especially specific business ones -- may still remain on some handsets in special cases. Presumably any additional devices that aren't updated will be phased out as new devices come to the market without Verizon Apps installed in the first place.
Source: Verizon Developer Community