What is your interpretation of "Silence-A Fable" by Edgar Allan Poe?

"Silence - A Fable" is one of Edgar Allan Poe's most brief, and yet most confusing, short stories.  The story is told by a Demon, who sits and observes the actions of a solitary man in a desolate, terrifying land.  Through the tale, the Demon attempts to provoke a reaction in the man, detailing his manipulations of the hellish, nightmarish landscape around the man.  The motive for doing so is unclear, but a close look at the tale allows us to understand the very clear message that Poe presents.

According to the Demon, the tale takes place in "a dreary region in Libya, by the borders of the river Zaire. And there is no quiet there, nor silence."  The landscape is the stuff of nightmares: waters are a "sickly hue,"  water lilies have "ghastly necks," and a "dark, horrible, lofty forest" forms the borderland.  Perhaps one of the most chilling lines is the demon's description of the elements: "It was night, and the rain fell; and, falling, it was rain, but, having fallen, it was blood."  The land is tumultuous; the language used to describe it conjures images of the Great Tribulation within the Christian Bible and could easily serve as the basis for countless end-of-days, post-apocalyptic scenarios that have been committed to print and screen throughout the last fifty years.

Perhaps what is most disturbing is the only other character that Poe introduces: the solitary man who sits down upon a rock.  Upon seeing the man, the Demon conceals himself, and watches intently.  Despite the terror around him, the man sits, only trembling but never losing his nerve.  The Demon begins to manipulate the elements, the landscape, and even conjures up beasts in an effort to terrify the man.  But no matter what the Demon does, the man remains.  Paragraphs 7-10 end with the same refrain:

And I lay close within my covert and observed the actions of the man. And the man trembled in the solitude; but the night waned and he sat upon the rock. 

The Demon's frustration is palpable; no matter what he tries, the man continues to sit and merely tremble.  It isn't until the Demon changes his tactics completely that he finally succeeds in his goal.  Eventually, the Demon ceases his tumultuous curses tries a new tactic:

Then I grew angry and cursed, with the curse of silence, the river, and the lilies, and the wind, and the forest, and the heaven, and the thunder, and the sighs of the water-lilies. And they became accursed, and were still.

Ultimately, this is the one thing that drives the man over the edge.  The demon observes:

And mine eyes fell upon the countenance of the man, and his countenance was wan with terror. And, hurriedly, he raised his head from his hand, and stood forth upon the rock and listened. But there was no voice throughout the vast illimitable desert, and the characters upon the rock were SILENCE. And the man shuddered, and turned his face away, and fled afar off, in haste, so that I beheld him no more.

It may seem strange that silence is the thing that causes the man to finally lose his nerve and flee in terror.  But this climax makes complete sense, given that it comes from Poe.  The writer fills his worlds with chaos and strife.  Even the initial landscape set up in this story is not known for quiet or silence.  The things that the demon creates are terrible, but they only accent the pre-established horrifying landscape.  The man upon the rock, while feeling uneasy, is able to maintain his sanity despite the ways in which the Demon adds to the "normalized" chaos around him.  This is symbolic of our own human tolerance for chaos and discord.  Because the world is loud and often chaotic, people grow used to it.  While they may get frightened, they tend to maintain their ability to function within the world, no matter how frenzied it may become. However, the idea of quiet, of absolute silence, is so foreign that when it appears, the human mind cannot comprehend it and tries to escape it.  Silence can be unnerving when people are not used to it.  In silence, the mind has a tendency to create all manner of horrible ways in which the silence will be broken, to the point where one may even choose to break the silence, feeling more comfort in sounds than in solitude.  Further, when there is little to worry about, to trouble the mind, people will often find things to worry about.  This is what happens to the man in the story; no matter what curses the Demon could conjure, his greatest curse on humanity is the curse of solitude and a restful mind.  The man quickly leaves, opting for any alternative to peace of mind.

This is the Romantic Poe, placing man alone in extreme nature.  Nature is perfect in and of itself, but when man is placed there alone he becomes terrified.  So we have a duality of nature: Garden of Eden (nature is perfect) vs. The Fall (man in nature realizes his sins).

Nature is much personified here:

For many miles on either side of the river's oozy bed is a pale desert of gigantic water-lilies. They sigh one unto the other in that solitude, and stretch towards the heaven their long and ghastly necks, and nod to and fro their everlasting heads.

There's three levels to the story: 1) the Demon telling the story to the man.  2) The Demon in the story watching the other man; 3) The man telling the story to us.  It is ironic that both men make the same mistake: this is why the Demon laughs.  Man becomes alienated from society in nature.  He ponders questions with no answers, and this terrifies him.  He realizes that death is the only haven from the heartless world.  The reality is this: nature lives on, while we perish all around it.

The lynx is a major symbol in the story.  It appears after the end:

And I could not laugh with the Demon, and he cursed me because I could not laugh. And the lynx which dwelleth forever in the tomb, came out therefrom, and lay down at the feet of the Demon, and looked at him steadily in the face.

The lynx has the last word here: its silence trumps the Demon's silence.  The lynx is, once again, a symbol of nature silencing man.

What is the significance of the title "Silence: A Fable" by Edgar Allan Poe?

There really is no one-size-fits-all method to derive the significance of a title of any short story. Nevertheless, the author has probably titled the story in a way to convey what the theme or topic will be.

Thus, it seems that your professor is trying to confirm that you understand the main theme(s) of the story. A careful reading and thoughtful analysis of what the author is trying to say is the best way to convey your understanding of the story and the significance of its title. It is also important to remember that the analysis is just one interpretation of the story and significance of the title. Other readers might have different interpretations that are justified as well. That is why explaining your thought process is important.

Understanding the author’s overall style can also help. For example, thoughts about the author’s writing style and themes of the writer’s other content come to mind regarding the short story cited in the question: “Silence: A Fable” by Edgar Allan Poe. Poe was the master of the macabre and stories with dark themes. Therefore, the word fable in the title suggests the possible use of irony, as readers generally associate the word with lighter stories such as fairy tales (which also have darker underlying meanings) and Aesop’s fables.

In fact, Poe’s story commences with the introduction of “the Demon” and, not surprisingly, soon introduces words that a reader would expect from Poe, creating a dark vision of the world in the story. The Demon refers to the “accursed earth,” “melancholy temples,” “dreary region,” and “sickly hue,” among other bleak surroundings.

The narrator tries to decipher the characters on a rock and reads the word “DESOLATION.” Then the narrator sees a man with the “features of a Deity” who is worried about and disgusted with mankind and “longing after solitude.” After a tempestuous and climactic storm, the universe in Poe’s story has changed, the characters on the rock now read “SILENCE” and the man flees, presumably in terror.

What is the fable—or moral—of Poe’s story? Many interpretations are possible. Poe might refer to the need for man to change. Poe describes the Demon and contrasts this evil being with a more human-seeming creature who resembles (but probably is not) a deity. The human creature worries about mankind and is disgusted at man’s collective actions. As he contemplates this, a storm rises up and the message on the rock changes from “DESOLATION” to “SILENCE.”

At least there is still an opportunity for second chances and redemption when the state of nature is “DESOLATION.” With “SILENCE,” however, it seems that the opportunity for redemption is over, and the deity-like man flees. Poe might also refer to the man's quest for solitude, but there is fear of too much solitude once the world shifts from “DESOLATION” to “SILENCE.”