There are actually two possible themes for this short story.
The first underlying theme is the evil that we have within ourselves is often worse than the evil that might be seen from outward appearances. This is a theme in the story because the old man is clearly ugly and has a revolting eye (which causes the narrator to do what he does in the story. Other than his physical being looking evil, the old man is seemingly harmless to others. However, it is the narrator who has the evil within him that allows him to murder the old man for absolutely no reason.
The second theme is that our guilt sometimes gets the best of us. After the narrator kills the old man, he hears a continuous beating, which he can not identify. This noise drives him insane to the point that he gives himself up to the police officers without even being questioned. Therefore, it was the build up of guilt within the narrator that forced him to admit to his crime.