Local notifications and push notifications allow the application to send information to the user while the application is in the background. The information could be a message, an impending calendar event, or new data on a remote server.
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On Android, the application requires a Service to send and respond to local notifications in the Notification Center.
On iOS, simply call the Titanium.App.iOS.scheduleLocalNotification method to have the application schedule a notification.
Starting with iOS 8, the application can create an interactive notification, where users are presented options to choose from in the notification. The user can respond to the application in the notification without opening the application.
Push notifications allow you to send a notification from a server to all devices that have your application installed on them, which are subscribed to receive push notifications. The device requires a connection to the internet to receive a push notification.