PlayStation Mobile is/was a store for the PS Vita and select Android smartphones, offering up indie games and PlayStation classics. But in July 2015, Sony will completely shut it down, after being released to the public in October 2012.
Sony has also said that as of September 10th, previously purchased games won't be able to be downloaded again. But not all is lost, you'll still be able to play games, so long as you activate your devices. You can find all the details of how to do this on the PlayStation website.
It's believed that the shutdown is due to a poor adoption rate, which was evident last year when Sony dropped support for Android phones running 4.4.3 or newer in 2014.
The news doesn't affect Remote Play though: PS Vita owners will still be able to mirror PlayStation 4 games when connected to the same network.