#2 has given us a very definitive exploration of this important term. I suppose we associate it mostly in terms of our discussion of tragedies and tragic heroes, who have some kind of tragic flaw that is often based on hubris or arrogance. Knowledge of this term helps us analyse famous tragedies such as Oedipus Rex, and also gives us an interesting way of looking at Shakespearian tragedies such as Macbeth and Julius Caesar. The tragic flaw that all of us are prone to, and is something of a human condition, is of particular relevance in these two tragedies, as basically good characters slowly become seduced by darker forces.
Funny, a lot of people must be reading "Poetics". I just answered another posting about this very subject. So, to start off the discussion, I am going to paste the answer I posted earlier so as to give others the chance to offer their own views on the subject.
The term hamartia was introduced in Aristotle's Poetics. According to Aristotle, the term refers to mistakes, sins, to err, and wrongdoings. Aristotle used this term to define a wrong committed against another person.
Over time, like many words, the meaning of hamartia has changed. Many critics have stated that Aristotle used the term wrongly in his text and that the true meaning of the word was more geared toward the err one commits when he/she does not know any better.
Aristotle's use of the word tended to lean towards the tragic flaw of a person based upon their own limits or weaknesses. While similar to that of alternative views, Aristotle's meaning encompasses that the flaw does not concede to the fact that the one in error is not wholly innocent and one cannot find him less morally at fault.