How do you terminate the current Unity app on the iPhone or Android? How do you make an app close itself?
Hit the Home button, or whatever the Android equivalent is. I don't know anything about Android, but iOS apps do not have any sort of software quit options.
Apple's policy does not allow this. You should always use the Home button. If you want to prevent an app from continuing to run in the background (although it's being paused then) after hitting Home, search the web for UIApplicationExitsOnSuspend. Setting this will quit the app when pressing Home.
EDIT: Haven't worked with Android yet. If Application.Quit() is not ignored on Android, and the application keeps running when hitting the Back button, you can try to quit the app in OnApplicationPause(), but not sure.