The two outstanding symbols in the story are the eye and the heart. The narrator's constant references to both makes it clear that they are central to the story and its dramatic development.
It is the old man's eye that, from the outset, is clearly a symbol of the narrator's deepest fear and his obsession. He despises the eye for it represents something malicious and epitomizes all that he dreads. He describes it as "...the eye of a vulture" and "--a pale blue eye, with a film over it." Both these descriptions make it clear that the narrator associates the eye with malevolence. Vultures are associated with death and decay for they feed off carrion, while the fact that that the eye has such an unusual color and has "a film over it" suggests something inhuman and supernatural. The old man is described as benign, but the narrator is overwhelmed by his strange eye and states:
...it was not the old man who vexed me, but his Evil Eye.
Whenever the narrator perceives the eye, he is violently disturbed and he plans to kill the old man, thus removing the eye from sight forever. On the evening of the planned murder, he describes the overwhelming effect it had on him:
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 in my bones; but I could see nothing else of the old man's face or person: for I had directed the ray as if by instinct, precisely upon the damned spot.
At this point the narrator also becomes aware of something else: the beating of the old man's heart. Just as the eye became an obsession, so too does the beating heart. It is the continuous pounding of the old man's heart that drives the narrator to utter madness. He leaps into the room and kills the old man, believing that he must silence the heart so no one will hear it.
The beating heart, at first, is a symbol of the old man's fear. The narrator mentions:
...there came to my ears a low, dull, quick sound, such as a watch makes when enveloped in cotton. I knew that sound well, too. It was the beating of the old man's heart.
...the hellish tattoo of the heart increased. It grew quicker and quicker, and louder and louder every instant. The old man's terror must have been extreme! It grew louder, I say, louder every moment!
It also symbolizes the narrator's own fear, especially of discovery, because in his mad state he believes that everyone else can hear the man's heart beating. He imagines the heart beating louder and louder and thinks that the increased volume will wake others and he will be caught.
In addition, the narrator's compulsive obsession with the sound of the old man's heartbeat foreshadows later events when he becomes overwhelmed by the belief that he is still hearing the heart and thinks that his interrogators can hear it too. He is overcome by his delusion and confesses to his crime.
It is easy to surmise that it is the narrator's guilt that, as the title suggests, forces him to reveal his crime and that the incessant, ever louder heartbeat he hears is a symbol thereof, but it is more his own depravity, inner malice and insanity that betrays him. He does not present even a smidgen of remorse.
The eye and the beating heart, therefore, are, in addition to the above, also symbols of this.