What is a “Push Notification” or “Local Notification”?

A generic “notification” allows an app to notify you of new messages or events without the need to actually open the application, similar to how a text message will make a sound and pop up on your screen.  

A “push notification” is initiated by the app owner from a server.  The “push notification” message is then forwarded on to the mobile devices when they are connected to the network to display the notification.  For instance an app owner may send a push notification alerting the app owners to a new store or contest at a mall.

A “local notification” is initiated by the app itself based on pre-configured data in the app.  For instance an app might provide information on the local store opening hours for a mall when you are close to that mall.