When you create a new ASP.NET Web Application in Visual Studio 2013 you have the possibility to create a Facebook app. (This template existed before but was hidden inside the wizard for creating a ASP.NET MVC 5 project.)
This facebook template is designed to run inside the Facebook web site. As you see from the screen shot above is it using MVC and Web API as building blocks.
This template will be executed inside a Facebook Canvas Page. The functionality included in the template will help you with authentication, permissions, and accessing Facebook data. The Facebook functionality also has an extensibility model so that you can build your own storage providers and more.
Here is a tutorial to create the Facebook Birthday App.