Red dot (circle) next to the app name below the app icon on the iPhone Home Screen on iOS 8
An Orange dot next to an app normally means it's a beta version, as installed through Testflight. I have a couple of those at the moment, though one looks more red. Trying to find if there's a difference between an orange and a red dot, or if it's just an artefact of the colour of the background image that makes it look red.
The dot you see is actually an orange dot, with transparency. On dark backgrounds it seems like it's red. Try changing to a bright background.
Orange dots for all beta apps that are downloaded from TestFlight and blue dots for recently updated apps from App Store.