Narratology is the discipline that studies the structure and function of a narrative. "Exposition" is an element of structure within the the study of narratology. For the sake of clarity, "narrative" is anything that offers or presents a story with a sequence of events in which characters are involved. Thus the three of the indispensable elements of narrative structure are: (1) events, (2) chronological/cause-and-effect sequence of events, (3) characters who are (i) agents causing events or (ii) victims effected by events or (iii) beneficiaries who are benefited by events. Some other indispensable elements of narrative structure are narrator's voice and narrator's point of view (these are referred to collectively as "narrative mode"). There are several theories of narrative structure. One commonly taught in school is Freitag's Pyramid structure of narrative. Bear in mind however that Freitag's is not the only theory of narrative structure.
In Freitag's Pyramid (also called "Triangle") theory of narrative structure, the initial element of structure is called "exposition"; other structural elements follow while exposition is the initial element. What this means is that the exposition, in Freitag's Pyramid model, is the first thing the reader/listener learns in the narrative. There are two qualifications to this. The first qualification is that since narrative is defined as events-sequencing-characters, many things can offer narrative, including but not limited to billboard signs, advertisements in magazines, comic strips or comic books, true-life adventures (or misadventures) and news reports of natural disasters, think, for example, of the narrative followed by the reports of the 2011 Japanese tsunami and nuclear power plant meltdown. The second qualification is that Modernist and Postmodernist writers seek intentionally to undermine these narrative elements [scramble them up], especially chronological sequencing.
Knowing that these qualifications to narrative exist and that there are a number of theories of narrative besides Freitag's, the Pyramid offers exposition as the first step in narrative structure. What is exposition and how is it applicable to "The Tell-Tale Heart" by the genius of creepiness, Edgar Allen Poe? Exposition is the introductory material of a narrative, or story, in which the principle characters are introduced and in which the "backstory" or background information of the story is presented. The function of the exposition to to orient the reader/listener/viewer to the who and what of the story about to be told. The exposition can be complicated in some stories such as those that begin in medias res, in mid-event, because, in these, the backstory and introductory material may be delayed until after the immediate problem is resolved. For example, if a story starts during a Western shoot-out between Sheriff and bad guys, the exposition's introductory and backstory material will be delayed until after the shoot-out is settled.
In "Tell-Tale Heart," the exposition is spread out over the first three paragraphs and is complicated because it begins with a "frame" that complicates the chronological sequencing of the events. A "frame" is a story told in present, in the "now" of the story, about events that happened in the past, in the "then" of the story. In "Tell-Tale Heart," the narrator starts by questioning some unknown listener (not us) about why he is thought by the listener to be "mad" or insane. The rest of the paragraph adds to the introduction of this principle character, who doubles as the first-person narrator, and tells us about his personality traits: nervous yet calmly narrating, acute sensory perception, not mad. The second paragraph tells the backstory about the old man who "had never wronged" him, but whose eye was an offense, and introduces the conflict: "I made up my mind to take the life of the old man, and thus rid myself of the eye forever." The third paragraph gives the implied setting: the house that the narrator and the old man share: "And every night, about midnight, I turned the latch of his door and opened it."
Thus we have from the exposition of "The Tell-Tale Heart," in the three opening paragraphs, the (1) principle characters, the (2) chronological sequencing within a frame story (a story told from within another story: e.g., I'm not mad: let me tell you a story to prove it.), the (3) setting, the (4) conflict integral to developing the plot and the (4) background story, or backstory.
The exposition of the story, the plot to murder an innocent man because of his eye: "He had the eye of a vulture --a pale blue eye, with a film over it. Whenever it fell upon me, my blood ran cold" unravels through a first person narration. The narrator is unreliable because he is insane and paranoid. This unique perspective gives readers insight into a psychotic mind, chilling them to the bone and making the story unpredictable
Setting: Early Morning- Eight Nights
Characters: Old Man- The Narrator
Tone: Horror, Scary, Horrifying