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.