There is a notion of a ViewModel, but it is not generally associated with Asp.net MVC. MVC uses the Model View Controller patter, where the controller handles interactions, builds up data from the Model, and then passes that data to the View for display.
ViewModels (and the Model View ViewModel pattern) is more generally associated with Silverlight and WPF. Xaml is a bit different in that the views can do two-way binding to the ViewModels, so the technology is a little different. For example, if you bind a textbox to a field, as you type into that textbox, the value of the field is updated dynamically. This sort of interaction isn't really possible in web pages since web pages are stateless.
The similarity in the two patterns is that they are both trying to separate the logic from the display. The most common use/reason for this is testing: you want to be able to perform from code (via a testing framework) all the interactions that a user will invoke via the User Interface.