The Narrator is speaking of a an who has done nothing wrong to him but he is haunted by his odd eye. His vulture like eye with its pale blue color. That is why he says this. "I made up my mind to take the life of the old man, and thus rid myself of the eye forever."
The narrator tells how he so cautiously crept into the man's quarters for 7 nights and he shone his lantern upon his eye, but it was always closed, so he just lwft as it was not the man who he wanted to kill but his eye as he says. "I found the eye always closed; and so it was impossible to do the work; for it was not the old man who vexed me, but his Evil Eye."
On the 8th night he is watching the old man waiting to get revenge on the eye, when he slips and wakes the old man, now the eye is open and the narrator can strike. The old man, still trying to convince himself the noise was just the wind, was wrong.
The awake man, startled by the narrator's scream as he yells and kills the man with the bed. After the heartbeat stops, the narrator states this, "First of all I dismembered the corpse. I cut off the head and the arms and the legs. I then took up three planks from the flooring of the chamber, and deposited all between the scantlings."
The Police arrive, as they were reported of a scream, the narrator lets the officers in and he convinces them that nothing is wrong and the old man is away. They believed him and stayed a while, long enough for the man to get impatient and is driving himself mad hearing the dead mans heart beat, until, "Villains!" I shrieked, "dissemble no more! I admit the deed! --tear up the planks! here, here! --It is the beating of his hideous heart!"