This is an interesting question, best answered by yourself, since only you know what you have learned about human nature from the story. To lead you in the right direction, consider asking yourself some questions about the story, and the narrator. For example, think about guilt. What role, potentially, does guilt have in the story, and what does that say about the impact that guilt has on human beings? Could the heartbeat the narrator hears be a manifestation of his guilt at having murdered an old man? When we feel guilty about things, what is our reaction? Are we noticably defensive? Do we feel compelled to confess, just to get rid of the guilt? Isn't our guilt like a constant weight or reminder of things that we have done, almost like the heartbeat was for the narrator? So, there are some conclusions that we can draw about guilt.
Also consider the narrator's motive. Setting his potential madness aside, think about how fixated he become on the old man, and how infuriated he was with him over something as ridiculous as his eye. Don't we too, sometimes, become fixated and angry over stupid, seemingly nonsensical things? Think about the last argument you had with someone; was it over something that really mattered? Or, do we as humans, tend to get offended, upset, and fight over minute and insignificant matters? And then, in anger, do things that we regret? There are some connections there too.
One last thing to consider: defensiveness. The narrator is obsessed with proving that he is not mad, that he truly isn't crazy. It almost seems as if someone has just accused him of being crazy, and his telling of the tale is an entire rant against it. How do we react when we are accused of something? Do we too react defensively, listing all of the reasons why that accusation is not true? Do we get all offended and huffy, thinking, "Well, how dare they!" and spend hours obsessing over our possible counter-arguments? Do we go home at night thinking, "Oh, I should've said that! That would've gotten them!" So, try to make some connections to people's reactions to accusations of an unflattering nature.
All of these things don't really paint a pretty picture of human nature, but hey. It's not a very warm fuzzy tale, is it? Entertaining, but not a very positive reflection of human nature. If we look closely, we can see some commonalities; hopefully in our case though, we keep things in check and don't murder someone and bury them in the floorboards...