I believe that the basic premise of this story is simple: one has to be able to live with oneself. It could also be interpreted as "don't do anything you might live to regret."
In Poe's story, the narrator murders an innocent man. The narrator's guilty conscience leads his already psychotic paranoia to become overwhelming; he believes that he can hear the heart of the victim beating, though it is hidden under the floor. Eventually, he confesses to the murder, although policemen who are in his apartment are obviously unaware of the truth. Had the narrator not done something his conscience could not handle, he would have been in no trouble, which is often the case in real life.
This short story is about an insane man who kills the old man he lives with because he hates the man's blue eye, which he calls an evil eye. The story is told by the insane killer, and Poe gives us a look into the mind of a truly disturbed person. He carefully plans the old man's murder, sneaking into his bedroom each night until the old man opens his eyes, revealing his evil eye. The killer chops the old man into pieces and hides him underneath the floor. Police come to the door because a neighbor heard the old man scream, but the killer invites them in, telling them that he had been the one to scream out. The rest of the story is spent in the mind of the narrator until he can no longer stand the beating of the old man's heart. He then confesses to killing the old man.