The following definition is derived from The Bedford Glossary of Critical and Literary Terms.
Generally, the original model from which something is developed or made; in literary criticism, those images, figures, character types, settings, and story patterns that, according to the Swiss analytical psychologist, Carl Gustav Jung, are universally shared by people across cultures. Archetypes, according to Jung, are embedded deep in humanity's collective unconscious and involve racial memories of situations, events, and relations that have been a part of human experience from the beginning. These not only manifest themselves in the subconscious material of dreams, but are also persistently expressed in the more consciously constructed material of myths and literature. Jung postulates that when an author recounts a narrative based on such unconscious memories, the reader's mind is subconsciously stirred, producing a singularly powerful psychological effect because the memories evoke primordial feelings, concerns, and responses that cannot logically be explained.
Examples: The snake is an archetypal image (or figure); so is the Trickster. The Flood is an archetypal image persistently expressed in the Myths and literatures of most of the world's cultures, even as the Savior (Messiah) is an archetypal personage. Like Easter, the Hindu observance Mahashivarati celebrates deliverance from death. The day commemorates the sacrifice of the god Shiva, who drank a poison that would otherwise would have polluted the oceans and threatened the future of life as we know it.
Mr. K's interpretation of "archetype":
An archetype, in my mind, is a symbol that has become ossified and solidified in the minds of people, no matter what their background might be. For example, the archetype of the Hero is a common one whether one is from Asia, Africa, or Europe.
As such, the hero archetype that is present is several of these films "conforms" to certain heroic traits:
Neo (MATRIX) does not know he is "The One"; he is reluctant to behave as a hero, denying his heroic qualities, is wounded, dies, then is reborn.
Harry Potter does not know that he is not a Muggle but in fact a powerful magic user; unlike Neo, he is happy to embrace his wizard/witchcraft heritage, has a symbolic wound in the form of a lightning bolt.
Luke Skywalker does not know that his father is Darth Vader; unlike Neo, he is happy to embrace the Jedi ideals, but not the basic ideal of friendship; he is wounded in having his hand chopped off by his father (whose hand gets chopped off by the son).
Frodo Baggins does not know that he and his friends will become instrumental in saving Middle Earth; he suffers mightily in his quest to destroy the One Ring; he is wounded even despite having the magical Elvish mail.
All of these individuals have a redemptive quest; the "archetype" involved is their commitment to the quest itself and their status as heroes.