In his Poetics, Aristotle outlined the ingredients necessary for a good tragedy, and based his formula on what he considered to be the perfect tragedy, Sophocles's Oedipus the King. According to Aristotle, a tragedy must be an imitation of life in the form of a serious story that is complete in itself; in other words, the story must be realistic and narrow in focus.
A good tragedy will evoke pity and fear in its viewers, causing the viewers to experience a feeling of catharsis. Catharsis, in Greek, means "purgation" or "purification"; running through the gamut of these strong emotions will leave viewers feeling elated, in the same way we often claim that crying might ultimately make you feel better.
Aristotle also outlined the characteristics of an ideal tragic hero. He must be "better than we are," a man who is superior to the average man in some way. In Oedipus's case, he is superior not only because of social standing, but also because he is smart: he is the only person who could solve the Sphinx's riddle. At the same time, a tragic hero must evoke both pity and fear, and Aristotle claims that the best way to do this is if he is imperfect. A character with a mixture of good and evil is more compelling that a character who is merely good. And Oedipus is far from perfect; although a clever man, he is blind to the truth and stubbornly refuses to believe Teiresias's warnings. Although he is a good father, he unwittingly fathered children in incest. A tragic hero suffers because of his hamartia, a Greek word that is often mistakenly translated as "tragic flaw" but really means "mistake". Oedipus' mistake - killing his father at the crossroads - is made unknowingly. Indeed, for him, there is no way of escaping his fate.
The focus on fate reveals another aspect of a tragedy as outlined by Aristotle: dramatic irony. Good tragedies are crammed with irony. The audience knows the outcome of the story already, but the hero does not, making his actions seem painfully ignorant in the face of what is to come. Whenever a character attempts to change fate, this is ironic to an audience who knows that the tragic outcome of the story - as they know it in the myth - cannot be avoided.