ASP.NET MVC uses a different design pattern than webforms. MVC aims to separate the different concerns into different layers.
ASP.NET MVC has some nice things out of the box for you, like scaffolding (basically you feed it a data source and it generates a basic form for you) and URL rewriting. You can, of course, do this with webforms, but MVC does it out of the box for you, which is nice.
In ASP.NET MVC gives you more control of the markup (or at least more easily gives you control of the markup). For many people this is a real nice-to-have. That said, you also lose some of the things that make ASP.NET webforms easy to work with, like ViewState.
Also, I'd like to add that you can mix and match webforms and MVC, so its not a "all or nothing" situation.
Hope that helped.