The murderer is what one might call paranoid. In his delusions, he thinks the old man who is blind, probably with cataracts because his eyes are clouded, is watching him all of the time. Because of his paranoid delusions, he ends up killing the old man by smothering him with a matress or pillow.
When the detectives were in the room searching for the old man, the paranoid murderer's own heart kept beating harder and faster. Again, being paranoid, the murderer assumed that it was the heart of the man he had killed and buried under the floor. Because he could not stop the pounding of the heart, the murderer ends up ripping up the floor boards to deliver the body to the detectives.
Poe gives the reader a first-hand visit into the mind of the madman. His details and delivery of the story lead us through the psychological horror story. Poe called this type of story an "arabesque".