First, that setting is enforced by the OS (so it's not for the app to decide whether to observe that setting). Put in easy words: Android won't let an app access the network unless it's running in foreground (i.e. the user is interacting with it) with the restriction enabled for it.
Explained with a plastic example: Restrict background data on the Google Play Store app (as I did), it won't anymore check for updates in background while you are on mobile data. But it will do so when you're using WiFi. Also, when you call up the app to install something, it will work as long as you keep it in foreground (i.e. not switch to another app while it's still downloading).
NetworkPolicyManager
adds an extra constraint that the screen must be on. "The user is interacting with it" suggests that you must be poking the buttons or something, but actually the activity just needs to be visible on the screen with no other app's activities on top of it. – Dan Hulme Oct 26 '13 at 22:51