It is a Greek word. Literally it means missing the mark. It is translated sin in the English Bible.
In Greek tragedy, "hamartia" refers to a fatal flaw in a character that leads to their downfall. It is often translated as "tragic flaw" and represents a mistake or error in judgment that ultimately causes the tragic hero's downfall.
Hamartia is when a character in a play fails to control his or her anger. Because of this, he or she loses everything. An example of this would be Romeo killing Juliet's cousin because he killed Mercutio. Because of this, Romeo ends up losing everything.
The biggest example of harmartia is Odysseus' act of hubris when he tells the cyclops Polyphemus his true name. This enables Polyphemus to ask his father Poseidon to curse Odysseus, and give him difficulties on his journey home.
A tragedy has a main protagonist who has a harmartia (a fatal flaw) which causes their downfall. The act of the tragedy has to be fast, usually ending with one or more sudden deaths. The main character should also have a huburis, or an inflated sense of self. A tragedy needs a father figure, a mother figure a hero and an antagonist. For example, in Hamlet the father figure would be the ghost of Hamlet's father, the mother figure would be his mother, the antagonist would be Claudius and the Hero would be Hamlet. All of that hokum was put forward by Aristotle, who had seen Sophocles's play Oedipus Rex, and proceeded to define tragedy based on it. In fact, a tragedy only needs to be story of someone which ends in a way that we feel sad or regretful, so that we say, "What a waste!" or "I wish that had turned out differently". No hamartia, hubris, mother or father figures are required. An antagonist is not even required.
Hamartia is the name of a game that literary critics used to play and high school English teachers still do. It is based on the notion that "tragic heroes" have a "tragic flaw", which is what harmartia means. It goes like this: select a character from a play. Do they die in the play? If yes, carry on, they might be a tragic hero. Then you can do one of two things: First, you can identify some characteristic about the character you don't like and call it a tragic flaw. Don't worry, nobody is perfect so you can find flaws in anyone. Or, you can imagine how the character might have lived if only he had done something different. Then you call whatever he did do a tragic flaw. OK, let's play the game with Julius Caesar. Let's look at Brutus--yes, he dies, so he could be the tragic hero--so what could he have done differently to avoid dying? I know! he could have been cynical and ruthless like Cassius. So we can say his tragic flaw is that he is a poor judge of character and trusts too easily. Oh, but hold on. Cassius dies, so he could be the tragic hero. Well, what don't we like about him? Aha, he's cynical and ruthless. So that's his tragic flaw. What about Julius Caesar? He dies too. Oh, but he's so arrogant and proud. There you go, a tragic flaw. (Arrogance and pride are favourite possibilities for the hamartia game. They are sometimes called hubris. In ancient Greece, hubris meant setting your will against the gods' but since that doesn't happen too often in literature these days, and the name is cool, hubris has been basically redefined as cockiness, or "tragic pride". Since a lot of the characters in tragedies are leaders, they are guaranteed to have this characteristic.) Does anyone else die in Julius Caesar? What about Cinna the poet? Well, he dies because . . . uh . . .oh, well, he's not really a tragic hero anyway. (Whew! got out of that one!) Basically, hamartia is a totally useless concept for understanding Shakespearean tragedy, because it is imposed upon the work by teachers and was not used by the dramatist to build his dramatic structure. It's only a game, and as a timewaster, you can probably find more entertaining games on your cellphone.