This setting appears when you’ve installed an application from the App Store that uses the Apple Push Notification service.
Push notifications are used by applications to alert you of new information, even when the application isn’t running. Notifications differ depending upon the application, but may include text or sound alerts, and a numbered badge on the application’s icon on the Home screen.
You can turn notifications off if you don’t want to be notified or want to conserve battery life.
Tap Notifications and turn notifications on or off.
Tap Notifications, then choose an application from the list and choose the types of notification you want to turn on or off.