I would like to contribute an example of exposition from the opening of the first chapter of A Tale of Two Cities by the great Charles Dickens. 

IT WAS THE BEST of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way—in short, the period was so far like the present period, that some of its noisiest authorities insisted on its being received, for good or for evil, in the superlative degree of comparison only.

I especially like this section of that marvelous opening:

it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair,

This is very abstract exposition. It seems to apply to the people of France, England, as well as other countries, including the United States. Possibly it says more about the French Revolution and the entire period surrounding it than many entire books on the subject. It is a pleasure to read that whole passage aloud, even if there is nobody else to listen. Dickens must have read it many to audiences in Great Britain and America when he was on his tours. What a thrill it would have been to hear Dickens himself reading his own words!

A good way to understand exposition is to examine a story that contains little or no exposition. One such story, which is frequently discussed in eNotes, is Ernest Hemingway's "Hills Like White Elephants." The reader is put in the position of an onlooker and an eavesdropper, wondering who these people are, where they are coming from, where they are going, whether they are married, what the problem is. All these questions would have been answered by a writer like Anton Chekhov, whose short story "The Bet" is full of the most detailed exposition, as is his longer story "The Lady with the Pet Dog."

Hemingway's "Hills Like White Elephants" is experimental. He wanted to see how much detail could be left out. He bragged about leaving explanatory material out of his story. He did the same thing in his well-known story "The Killers." No one will ever know what Ole Andreson did to make someone want to have him killed or how they knew he was hiding out in the town of Summit. The virtue of stories like Hemingway's is that they get right into the dramatic part of the story. "The Killers" has a wonderful opening sentence:

The door of Henry's lunch-room opened and two men came in.

Who are they? Where did they come from? What did they want?

Think of conventional plot as a three-part entity: beginning => middle => end. The function of the beginning is to present an initial, usually stable situation as well as the probabilities and necessities from which flow a rupture of that stability, an exacerbation of the problem (plus efforts made to solve it), and definitive solution that follows logically from the foregoing materials. (Some plots, of course, have no logic to them at all or fail to achieve closure, or end in unprepared surprises. They need not concern us here.) The exposition encompasses the beginning of the plot, but it is not necessarily represented at the beginning of the text. Indeed, the latter may open in medias res, somewhere in the middle, and the reader must reconstruct the beginning from "expository" clues given chiefly in the middle but also (as in classic detective fiction) at the end. 

The exposition is one of the seven elements that construct a plot and can be charted on Freytag's pyramid.The exposition of a story or play is found at the beginning of the text. In the exposition, the reader is introduced to characters by means of description. The exposition may reveal both the physical and personality traits of characters. The exposition is the foundational block by which we will identify characters later in the story as either protagonist or antagonist, either flat or round, either static or dynamic.The setting is also revealed in the exposition. The setting will tell us both the time and place of the story. It may also reveal the mood of the story. Thus, the exposition is the first step to creating a dynamic and well written story.

Exposition is one of the four chief types of composition.  The others include argumentation, description, and narration.  In high school as well as English 101 and 102 of your freshman year in college, you can expect to write papers which fall into each of these categories.

The purpose of exposition is to explain something, and this may be done through several methods.  A few of the methods include identification, definition, classification, comparison and analysis. 

In drama, the exposition is the introductory material which creates the tone and mood of the piece, creates the setting, introduces the characters, and supplies other facts the reader/audience needs in order to understand the development of the plot and character motives. 

The part of the story, usually near the beginning, in which the characters are introduced, the background is explained and the setting is described. Stories can work against the expectation of expository material being placed in the beginning. Stories that begin in media res (inthe middle of things) play against the expectation of the audience. Poe’s “The Pit and the Pendulum” provokes the reader to decipher expository facts. This raises the anxiety and attention level of the reader.

I teach my students that the exposition accomplishes three purposes: provides background information, establishes the setting, and introduces the characters.  The exposition ends with the inciting incident, the point at which the action begins and the complication (or rising action in a drama) begins. Depending on the length of a work, the exposition may be a few paragraphs or several pages.

Exposition refers to the opening information in a literary piece. It also refers to the introduction of the theme in a piece of literature. Basically the reader gets much needed information about the work from the exposition usually given at the beginning to set the stage for the work. After the exposition is given to the reader the rising action begins to unfold leading to the climax, or the highest point of action in a story. Following the climax is the falling action where the conflict is set to be resolved and finally the resolution is put forth and the work is concluded.