There are various definitions for archetype. For Example, Carl Jung says that an archetype is "a preconscious disposition that enables a man to react in a human manner". I don't think that is an accurate definition for an archetype because archetypes have nothing to do with human psychology. I think archetypes are related to the problems and questions a society has and the way they solve or answer them. So archetypes are human patterns of ideas or feelings present in a story or narrative. That is why archetypes are common in towns all over the world because they have similar ideas when solving a problem or answering a question.
One common archetype is the figure of Tyler Durdan, and it is featured in the movie "The Fight Club". I think Tyler Durdan's character represents the shadow because he represents everything the main character (narrator) would want to be as well as all the narrator considers as wrong. Tyler represents the shadow because he is the doble personality of the narrator when the narrator thinks he is asleep. For Example, Tyler develops a plan without letting the narrator know. Here we can observe how the narrator looses control of his "dark side" and even acts without knowing that he acted.
This movie represents how the lack of sleep is very painful. So this archetype is essential for the story because without Tyler Durdan the viewer would not understand that insomnia broke the narrator into two different people, which lead the narrator to hurt himself. For example, Tyler asked the narrator "would you be happy if you died right now?"in a life or death situation. The narrator did not know the answer. Without Tyler in situations like this the viewer wouldn't understand the relation between the narrator and his "dark side".
In conclusion, the use of this archetype is important to the movie because it helps the viewer understand the relation between the narrator and his shadow. This situations where an archetype is essential in a narrative, story or even a movie are common because archetypes are the patterns that help the reader or viewer understand the role of each character or event.