Instead of focusing on the content of the text like both Structuralism and New Criticism do, Structuralist Narratology moves towards a different angle of the Structuralism theory and looks at how the text itself is executed. How has the author portrayed the text? From what perspective is the story being told and how does this affect the meaning? The way the author writes a piece can give us a lot about the piece itself. 
The best way to explain Narratology is through the explanation of Gerard Genette. Genette brakes down the term “narrative” into three subcatagories; story, narrative and narration. Story is the plot. The events that transpire in sequence to create, essentially, a story. The narrative is the words that the story is made up of. What the author actually types, or as Genette refers to it, “the actual words on the page” (215). Finally, narration refers to how the story is told and by whom. Another important “how” of Narratology, along with the narration, is tense. This is the narrative’s time. This includes the order of the events in the story, the period of time which certain events are given to be described and the repetition of events throughout the story.
I believe Narratology is a very important and interesting way to approach a text which can be used as a clue to reveal many things about the story. If we know the character working as the first-person narrator of the story is unreliable, we would read the text in a different way than if the narrator was third person, full omniscient. This theory, however, is somehow contradictory to New Criticism in that the narrator is sometimes the author.