Mobile apps can use Windows Azure Mobile Services to handle backend tasks like data storage, user authentication, push notifications, and more. The services provide a backend infrastructure without requiring backend code. Client SDKs support platforms like Android, iOS, and HTML/JavaScript. Server scripts allow custom business logic to be run during data operations. Push notifications can be sent directly to devices using services like GCM, APNS, and WNS. The demo shows creating a mobile service, storing and authenticating user data, and implementing push notifications on Android using GCM.