What do grayed-out app icons mean in iOS 7?
It's a glitch, where the grey overlay that appears on top of an app when you tap it is retained when you exit the app.

You can remove it by interacting with the app icon in some way, whether that be swiping between pages starting with your finger on the app, or simply tapping the icon.

It appears to be fixed in the dev build of iOS 7.1 :)