ASP.NET MVC is a framework that helps you build applications (note: I did not say web applications only) in a Model View Controller pattern. It breaks your applications presentation layer in to three distinct parts: The Model is the data. The View is the presentation. The Controller is the glue that holds it all together and manages interactions.
What this means is that you no longer have to build separate web services to expose application logic to consuming applications that do not want standard HTML. Those applications instead make requests and the ASP.NET MVC application is extended to process those requests and return whatever is required. The consuming application can be Windows-based, a mobile application, another web service or pretty much anything you can imagine.
There are a lot more differences between ASP.NET and ASP.NET MVC but this is an architectural one that will save you a lot of implementation time. Instead of wasting time on software infrastructure and scaffolding, you concentrate on writing business logic and exposing that business logic in consumable ways.
It is totally worth considering if you are have a greenfield project or are moving to later versions of .NET and are reconsidering ASP.NET.