"The Tell-Tale Heart" is told from the first-person point of view of the murderer. As he narrates the story, we experience the events as he understands them and wishes to present them. This makes him an unreliable narrator, and this unreliability is reinforced by his stated aim of telling the story to convince the reader he is not insane.
His narration is therefore ironic: while he is trying to convince us of his sanity, the actions he describes are those of an unhinged personality. First, he has a strange obsession with the old man he takes care of. He stalks and spies on him at night, and has a bizarre fixation with what he considers the old man's "vulture" eye. When he kills him, he offers no reasonable explanation.
Second, he becomes strangely convinced after the police arrive, search the house, and believe his story that he can hear the heart of the murdered man beating louder and louder under the floorboards and becomes equally convinced that the police can hear it too. This perception is clearly delusional.
His point-of-view also emerges from a sense of myopia that creates claustrophobia. We are placed very close to the action of the story while being given no context that would help us to make sense of it. Who is the old man? Why is the narrator his caretaker? Where does the story take place? This lack of detail adds to the nightmarish quality of the narrative.