What does the title "The Tell-Tale Heart" signify?

The title "A Tell-Tale Heart" refers to the constant sound of the heart beat that the narrator hears after he has murdered the old man.  The heart beat basically comes from the narrator's guilt-ridden conscience and leads him to turn himself in.

The resolution of the narrative occurs when the narrator, prompted by the incessant sound of a beating heart, can no longer contain his ever-increasing sense of guilt. The title signifies that guilt; the beating heart is a metaphor for the guilt.  Enotes has an excellent explanation of the entire short story,

The term "tell-tale" is probably old-fashioned and completely out of use today. A synonym commonly heard in schools is "tattletale." Roget's Thesaurus contains many synonyms, including "informer," "stool pigeon," "fink," "rat," and "whistleblower." The idea Poe wanted to convey in the title was that the sound of the beating heart informed on the murderer and caused him to be apprehended. It is hard to think of what adjective Poe might substitute for "tell-tale" if he were writing the story today. He might call it "The Double-Crossing Heart," "The Betraying Heart," or "The Judas Heart." (On the other hand, he might just keep his origijnal title.) The sound, of course, was purely imaginary. It was most likely the murderer's own pulse he was hearing because he was feeling nervous and his heart was beating abnormally fast and raising his blood pressure. 

The unnamed narrator lives with an old man who has a spookily cloudy eye.  The narrator appears to be crazy.  He puts up with the old man for a long time, but the eye drives him further and further over the edge of insanity.  Finally, one day, he murders the old man and buries his body under the floorboards.  When police come to investigate (neighbors had complained of strange sounds coming from the house), the narrator believes he hears the old man's heart thumping beneath the floor.  It sounds so loud to him that he confesses, screaming at the police:  ‘‘I admit the deed!—tear up the planks!—here, here!—it is the beating of his hideous heart!’’

It is called "The Tell-Tale Heart" because the heart, he believes, has betrayed him and told of the narrator's crime.

How does "The Tell-Tale Heart" represent a horror story?

Poe's story is a horror story both psychologically and physically.  Psychologically, we see the results of madness, how the mind can become so convinced of being persecuted that violence, and even murder, are justifiable.  You see this in the first paragraph of the story.  The narrator says, "The disease had sharpened my senses -- not destroyed -- not dulled them."   Despite his claims, it is clear that in his madness, he has convinced himself that the old man with whom he lives is out to get him. 

Other ways Poe creates an aura of horror is through his descriptions of the old man's "vulture eye":  "It was open -- wide, wide open  -- and I grew furious as I gazed upon it.  I saw it with perfect distinctness -- all a dull blue, with a hideous veil over it that chilled the very marrow of my bones."  Even worse is his description of the murder:  "The old man's hour had come!  With a loud yell, I threw open the lantern and leaped into the room.  He shrieked once -- once only.  In an instant I dragged him to the floor, and pulled the heavy bed over him.  I then smiled gaily."  The horror continues as he conceals the body in the under the floor boards. 

The tale returns to the psychological as the narrator's madness makes him think he hears the old man's heart beating under the floor boards, a sound that becomes so loud in his head that he confesses his crime. 

What could be an alternative title for "The Tell-Tale Heart"?

I would agree that your choice should be linked to the parts of the story which impact on you the most. I would select from "The Vulture Eye", 'The Madman in the Darkness", "Retribution", "The Pulse" or "The Tortured Man". The last suggestion could be ambiguous: both the old man and the narrator are tortured in the story.

What would be an alternative title for "The Tell-Tale Heart"?

How about: 'Be Still, My Beating Heart'?  This title says it all.  It names the heart, which is the central object of importance in Poe's short story.  It also commands that heart to be still, which, if that truly happened would signify death.  Therefore, it matches the idea of the murder in the story.  'Be still, my beating heart,' also means that the heart is pulsing rapidly because it is excited in some way (be it love, happiness, anxiousness, or fear).  So this fits the story because the murderer is certainly anxious and paranoid about having killed another man.

How does the title of "The Tell-Tale Heart" foreshadow its events?

The title of Poe's story foreshadows the demise of the narrator who suffers from psychological terror of the consequences of time. For one thing, the sound of the title mimics the ticking of a clock as well as the beat of a heart. At any rate, this beating of the heart symbolizes the persistence of time that the narrator is unable to stop.

In addition, the title of this story also foreshadows much of the repetition that prevails throughout the narrative. Moreover, the repetitions in the story become clues to the mystery. For, besides the repetition of the old man's eye, there are two other repetitions: the concept of time and the narrator's claim that he loves the old man. Therfore, the narrator has a certain identity shared with the old man, so when he kills the old man in order to be rid of the "vulture eye," death is not the end of the narrator's terror. Instead, his own heart, aligned with the old man and their shared terror of time, becomes the "tell-tale heart," and in his psychological torture, the narrator confesses,

Almighty God!—no, no! They heard!—they suspected!—they knew!—they were making a mockery of my horror!-this I thought, and this I think. But anything was better than this agony! 

Villains!” I shrieked, “dissemble no more! I admit the deed!—tear up the planks! here, here!—It is the beating of his hideous heart!”

It is, ironically, the beating of the narrator's own heart that tattles on him, not that of the old man, for, in killing the old man's eye, the narrator's "I" yet remains afterwards to answer the beating of his own "tell-tale" heart.

Can anyone explain "The Tell-Tale Heart" to me?

"The Tell-Tale Heart" whose title means "tattle-tell," is a story of psychological horror.  The narrator, a madman, kills a man and boasts of his skill in doing so without detection.  However, in his madness, the narrator believes that he hears the heart of the dead man beneath the floor boards where the narrator has buried his victim.  Obsessed with this "sound," which is probably the nervous beating of his own heart, the madman tears at the floor boards and cries out, "Disemble no more!" giving himself away to the police who have entered his house in order to investigate a shriek heard outside.

Of course, all the horror emanates from the mind of the narrator who becomes fixated upon the eye of the old man whom he claims to love.  But the filmed eye, like that of a vulture, he blames for his killing of the old man.  Also, the old man intuitively senses that some horror awaits him as he sits up in bed, groaning, long before the narrator attempts any harm. This interweaving or "arabesque" as Poe termed it, of symbols that change in meaning (the lantern, the eye) has led the critic James Gargano to believe that the story is a doppelganger. A doppelganger is an apparitional twin or counterpart to another living person.  That is, Poe's narrator and the old man are both of the mind of the narrator, who projects his terror and shares his terror.  This is why the narrator "hears" the beating of the heart of the dismembered, buried old man.

See the links below which will help with this concept of doppelganger.

What is "The Tell-Tale Heart" about and what symbols can be found?

The best way to do this is to read through the story, and try to shrink each paragraph down into one or two simplified sentences that summarize the main point of each. I'll give a brief summary below, along with links that will lead you to the story itself so that you can do a more detailed summary; space doesn't allow it here.

There is a man who becomes obsessed with an old man in his building with one bad eye that is filmed over.  He compares the eye to a vulture (a symbol of impending death and watchfulness) and learns to hate the eye so much that he ends up wanting to murder the old man.  He goes to the old man's room at night, opens the door a bit until his lantern can see the old man, and just watches him.  One night the old man awakes in the darkness, and the narrator goes in very stealthily and kills him.  He buries him under the floorboards in his dwelling.  The police come and start questioning him about the old man; the narrator is so confident in not getting caugh that he asks them in and sits down right on top of where the man is buried.  But then he hears what he feels is the old man's heart beating beneath the floorboards.  The beating gets louder and louder; the narrator is certain that the police can hear it!  He finally, when the beating is so loud he can stand it no longer, confesses.  The beating heart noise is a symbol of his own conscience for having murdered the man.

Define the title of "The Tell-Tale Heart."

Edgar Allan Poe is the master of thriller stories and horror stories. He focuses on the macabre in his writing.

The Tell-Tale Heart tells us that something about this story is going to involve a type of tattle tale.  It might be a romance, but based on what we know about Poe's history, we can presume that it will not be a romance as we understand it. We might presume that the conscience or "heart" tells on itself.

The title almost gives away the plot.  But we don't know whose heart is beating until the very end of the story.