What is significant about the time period that "The Tell-Tale Heart" was written in relation to the story?what did the time period have to do about...

I don't see any significant differences in how this story would be accepted by the reading public at the time of its publication and today. Poe's "The Tell-Tale Heart" will NEVER cease being one of the greatest short stories ever written.

Very little of the story's action would be altered by being set in the 21st century. Of course, there was no electricity; today, the old man with the evil eye would simply switch on the lamp on his nightstand and survey the room. Most newer homes have solid flooring, so tearing up the planks would be difficult. And digital watches do not tick, so the sound of the beating heart would have to be compared to something else. But the mood and building suspense that Poe creates has satisfied millions of readers in the past and should continue to attract new fans of his story in the future.

Actually, I should point out that it was somewhat unusual for a story of this type to have been published when it was (1843), since Poe virtually invented the genres of the horror and detective short stories, of which "The Tell-Tale Heart" is an amalgam. It was a new style of writing and Poe never profited from it in his lifetime. (He was paid $10 for the story.) So, yes, I suppose it was a bit ahead of its time.