Silverlight is another technology to write Web applications. It is a part of .NET 3/0/3.5. It is similar to ASP.NET and in future will replace ASP.NET. Instead of ASP.NET, Silverlight uses XAML as it's front-end and C# or VB.NET as code behind.
Here is definition from Microsoft:
Microsoft Silverlight is a cross-browser, cross-platform, and cross-device plug-in for delivering the next generation of .NET based media experiences and rich interactive applications for the Web.
By using Expression Studio and Visual Studio, designers and developers can collaborate more effectively using the skills they have today to light up the Web of tomorrow.