In this example the diagram below shows how the Azure Mobile Services platform can use hybrid connections to reach down on premise and access a database to retrieve some data.
The role of the Azure Mobile Services platform is to provide a back end to the mobile application allowing a great experience for developing mobile applications. When mobile services is combined with the Azure BizTalk Services Hybrid Connections capability this provides a way for the mobile developer to simplify their access to the on premise resource.
The developer is almost able to treat the resource (in the case of this example a database) as being a local resource on the same network, and access it via a connection string. The role of hybrid connections is to allow the developer to configure a connection which can reach through to an on premise agent which is able to connect to the real database. In mobile services the developer simply changes the connection string to point to a hybrid connections endpoint.
The overall benefit of hybrid connections in this architecture is to provide the simplest way to reach down to the on premise resource.
One of the other benefits of hybrid connections is that you are not limited to just accessing a SQL database. The fact that it works at the port layer should allow you to configure access to almost any service which you can access the port for.