Contrary to what many people believe, Silverlight is not simply a rich media player for the web. Nor is it just a replacement or a competing product for Adobe Flash. Silverlight is a technology that allows developers to deliver Windows-like rich user experience to the web. This includes animations, vector graphics, music, movies, etc., but it also includes the ability to develop WinForms-like applications with grids, treeviews, toolbars, and so on and so forth.
To get started with Silverlight, checkout these videos, or see this demo by Scott Guthrie and Jason Zander on the .NET Show. If you are looking to develop a WinForms-like user experience, you may also appreciate GOA WinForms which is an implementation of standard System.Windows.Forms .NET library for both Adobe Flash and Silverlight.