Microsoft Azure Mobile Services allow developers to build scalable backend services for mobile applications. It provides features like structured data storage, push notifications, authentication, and server-side logic. Azure Mobile Services offer elastic scaling, global availability, and consumption-based pricing. It pairs cloud computing capabilities with mobile development to overcome limitations of mobile devices like limited storage and compute. Examples of scenarios it supports include modern mobile apps, rapid development of apps with a secure backend, and apps requiring structured data storage in SQL databases. The presentation demonstrated how to create a Mobile Service and its REST API.