The DataContext of a FrameworkElement is what the element is bound to. It is fundamentally of type object. In the MVVM pattern, this is most frequently the ViewModel object, but it need not be. It is simply some context information you want to apply to that FrameworkElement. It does not directly affect the visual representation, by itself.
When WPF wants to display some object that doesn't have it's own visual representation (e.g. isn't descended from UIElement, it will look to see if a corresponding DataTemplate exists to define how it should present that data. In your example, you have said that the UserViewModel class should be presented using the UserView control, but you have not actually created either the UserViewModel or UserView.
These two concepts often go together. For example, imagine you had an ObservableCollection<object> which had in it a Foo and a Bar object. You could define different DataTemplates for Foo and Bar. Then you could bind your collection into an ItemsControl. Each object in the control would get a visual representation based on the appropriate DataTemplate from its type.
Another simple example: if you have a property on your ViewModel named DisplayObject and you simply want it to appear with whatever DataTemplate you have defined, you can use the ContentPresenter control:
<ContentPresenter DataContext="{Binding DisplayObject}"/>
Again, this results in WPF looking up the correct Template for the type and using that to construct a representation.