What is ASP.NET MVC and when should I use it?

This is a -very- broad question. Let me try to provide the "basics" and see if this helps in your learning journey.

ASP.NET MVC is Microsoft's implementation of the Model View Controller pattern for building web applications. The framework is built on .NET and leverages the ASP.NET (.ASPX) "view" syntax by default. It aims to enable web developers to build web applications with .NET that:

• Have better separation of concerns
  
• Are easily testable (encourage TDD)
  
• Give devs maximum control over rendered HTML

It is not a replacement for ASP.NET WebForms, but rather an alternative for developers that do not like some of the limits/patterns of WebForms. Microsoft also hopes to attract developers from the RubyOnRails crowd to .NET with this open source .NET framework (ASP.NET MVC is licensed under the MS-PL and the source is available on CodePlex).

For more in depth learning, check out these resources:
Official ASP.NET MVC Learning Pages
Scott Guthrie's Intro to ASP.NET MVC Framework

That's a good place to start. Hopefully from there you'll have a "foundational" understanding of ASP.NET MVC.