ASP.NET MVC is really an answer to Ruby, and the new, trendy, and (IMO) better way of decoupling the browser(client) from the server as much as possible.

ASP.NET Webforms gives you a lot of control over the client from the server side, with direct access to pretty much everything. Essentially your view and controller are one in the same, which gives you a lot of power, and most times a lot of mess.

ASP.NET MVC separates the view and controller by detaching the tight coupling of a .aspx file and the .aspx.cs file which accompanies them in webforms.

Essentially, the difference is having your much more (typically all) of the processing to display data to the view file, and leaving the business logic and the rest in the controller, keeping them both cleaner by convention, but also with less access to each other than webforms allows.