We really don't know what the exact setting is, so it's hard to say whether it has any significance. We know that the narrator is living with an older man. We don't know their relationship. Are they father and son? Uncle and nephew? Brothers? Boarder and landlord? The narrator says that he loves the old man, so they must be at least friends.
What is significant about the story is its tone. The feeling of nervous fear builds until the narrator almost explodes with his confession. The first-person narrative limits us to knowing only what the narrator thinks, but that is enough to create the suspense in the story.
It is a similar setting as "A Rose for Emily" which you may someday encounter. The inside of one's house is metaphor for the inner self. While investigators are poking and prodding through his house, he feels them investigating himself and his secrets. He has hidden just beyond the façade of his house an awful secret, just as he has in his soul. His guilt overwhelms his plans to hide his crime. He has a hidden monster as well as a hidden corpse and he believes the discovery of one will bring out the exposure of the other. The floorboards are not a sturdy enough boundary to hide his horrible secret.
I personally don't consider the setting of this story to be especially important or significant, beyond the fact that the old man lives with the narrator, which gave the narrator access to kill him. This particular story doesn't give as much setting detail as some of Poe's other famous stories and poems. Rather, it relies on the first-person narration of the insane murderer and everything that happened on the nights leading up to the murder of the old man and on the night of the murder itself.
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The significance of the setting is all about creating a mood. Many believe that the element of setting connects only to time and place. However, the mood and atmosphere also play a major role.The setting in the Tell-Tale Heart is dark and take place primarily at night when the victim is asleep. It doesn't take a stretch of imagination to get visual pictures from the text (a full moon with clouds drifting past or thunder and lightening crackling outside the window). These images are not included in the text but the reader can sense these images because of the mood created by Poe. If one really wants to understand the significance of the setting, try reading the story by a single dim lamp, late at night with all the other lights in the house turned off. scary!