Model-View-Controller is the concept introduced by Smalltalk's inventors (TrygveReenskaug and others) of encapsulating some data together with its processing (the model) and isolate it from the manipulation (the controller) and presentation (the view) part that has to be done on a UserInterface.
The model is used to manage information and notify observers when that information changes. The model is the domain-specific representation of the data upon which the application operates. Domain logic adds meaning to raw data (for example, calculating whether today is the user's birthday, or the totals, taxes, and shipping charges for shopping cart items). When a model changes its state, it notifies its associated views so they can be refreshed.
Many applications use a persistent storage mechanism such as a database to store data. MVC does not specifically mention the data access layer because it is understood to be underneath or encapsulated by the model. Models are not data access objects; however, in very simple apps that have little domain logic there is no real distinction to be made. Also, the ActiveRecord is an accepted design pattern which merges domain logic and data access code - a model which knows how to persist itself.
The view renders the model into a form suitable for interaction, typically a user interface element. Multiple views can exist for a single model for different purposes. A viewport typically has a one to one correspondence with a display surface and knows how to render to it.
The controller receives input and initiates a response by making calls on model objects. A controller accepts input from the user and instructs the model and viewport to perform actions based on that input.
An MVC application may be a collection of model/view/controller triplets, each responsible for a different UI element.
MVC is often seen in web applications where the view is the HTML or XHTML generated by the app. The controller receives GET or POST input and decides what to do with it, handing over to domain objects (i.e. the model) that contain the business rules and know how to carry out specific tasks such as processing a new subscription.