A push message is any notification from a smartphone app that displays while that app is not actively in use. Push messages are common on apps for iPhone and Android, and they frequently appear as pop-up dialogs, banners and small badges on each app's icon.
To change push message preferences on an iPod Touch or iPhone, the user taps the Settings icon on the home screen, then taps the Notification Center and goes to the Notifications page. The slider there is moved to the On or Off position.
Push notifications on Android are enabled by default, but the user disables individual apps from sending them. The user does a long press on the app's icon and then presses the App Info button. The user taps the Show Notifications box in order to disable it. The user repeats the process to restore that app's notifications.