Nature of the murderer

The murderer/narrator of "Tell Tale Heart" is, of course, mentally ill. But that doesn’t really get to the heart of the story, or why it is so effective. Poe's choice to have the murderer directly address the reader transforms our relationship to him. While it is not clear what the story’s context is (perhaps the reader is visiting the man in an asylum?), the net effect is for the reader to see things through the murderer's eyes. The narrator's point, of course, is to prove through the story that he has "full control" of his mind. From his point of view, his actions made sense—given his heightened senses, the old man's look became unbearable; his ability to plan the murder and hide the body, he claims, is evidence of his sanity. In a similar way, his confession to the police can be seen as a "reasonable" response to hearing the heart beating even though the man was dead.
It’s clear that Poe is giving us in the story the ravings of a mad man. But the challenge of "Tell Tale Heart" is to recognize that, for the man, there was a certain "reasonableness" to his actions, based in part on the evidence of his own ears. We may dismiss the narrator as crazy, but some part of the story poses, "What if he isn't?"

The murderer in "The Tell-tale Heart" is mentally unbalanced. He wants to convince his audience that he is sane, but all the actions he describes suggest a deeply troubled personality behaving irrationally.
He kills a man for no discernible, rational reason. He dislikes and is frightened of the old man's "Evil Eye," which appears to be a figment of his own imagination. He claims his hearing is "acute" and that he is terrified and disturbed by the sound of the old man's heartbeat. Therefore, he murders him.
He buries the body under the floorboards. When the police arrive, he appears to be getting away with the murder until in his own, deluded mind, he thinks he hears the heartbeat of the dead man pounding more and more loudly. He confesses his crime, not because he has been accused by someone else or presented rational evidence of it, but because he is living in his own world of fear and torments, divorced from reality.