Models are your domain. For example we might have a customer model. We can use this customer in our domain. We can place orders for this customer. We can update the customers contact details, and so forth.
// Domain object, encapsulates state.
class Customer
{
public void PlaceOrder() {...}
public void UpdateContactDetails() { ... }
}
View Models are a way of presenting the data in an easy way. For example, we might have a customer view model. This would be a simple DTO (Data Transfer Object) which allows us to expose the customer to a view. Often view models are created from models - some form of conversion often takes place.
// DTO - exposes state - no domain logic
class CustomerViewModel
{
public string Name { get; set; }
public int Id { get; set; }
}
The benefit of using a view model rather than using your domain objects in your views is that you don't have to expose the innards of your domain to ease presentation logic. I should add that view models are a way of controlling model binding, e.g. if you expose a database record you probably don't want the whole record to be bindable. Using a view model means only those parameters on the model will be bound. Therefore using view models is important from a security point of view. The alternative here is to use whitelists to control what is used during the model binding process - naturally this is tedious and prone to error.
In terms of ASP.NET MVC - the word model is used somewhat interchangeably. In a "real world" project, your domain is likely complex and will not reside inside a Web App, chances are you'll include some other dependency. Therefore the "models" you'll use will be View Models.