MVVM stands for ModelViewViewModel.
MVVM Light is a made up thing from "Laurent Bugnion" - GalaSoft
http://mvvmlight.codeplex.com/
MVVM is an enterprise application development pattern,a best practice. We can deep dive in by following page.
http://msdn.microsoft.com/en-us/library/gg405484(v=pandp.40).aspx
If you would like to do whole business dedicated. Independent from User Interface elements such as silverlight TextBox, we need to apply MVVM pattern.
By this way we reuse business part for other client platforms. Such as Windows Phone ..
If you know MVC you can resample Controller to ViewModel but this ViewModel does not contain any reference of objects in your view. And your VM may abstract your View.
I think an MVVM pattern applier for .NET should be aware of these technics;
Commanding,
CollectionViewSource for filtering sorting operations,
DataContext,
Binding,
INotifyPropertyChanged