The fall of MacBeth and Lady MacBeth after murdering King Duncan in order to usurp the throne is the primary element that classifies "MacBeth" as a tragedy. A tragedy is defined by the fall of a hero through hubris that is usually predicted by supernatural forces.
MacBeth is a high-ranking military man and nobleman who wants to inherit the throne of Scotland. He and his wife concoct an increasingly murderous plot in an attempt to make his aspirations come true. MacBeth's hubris is that he believes himself capable of getting away with murder. The trio of witches serve more or less the same purpose in MacBeth as gods or goddesses do in Greek tragedy by predicting MacBeth's failure and ultimate downfall. They first predict MacBeth's success by playing into his pride and then use that pride to illustrate why MacBeth's chosen path will lead only to destruction. Ultimately, like the heroes of Greek tragedy, MacBeth is ambitious, but he is also proud and ultimately falls victim to his own shortcomings rather than choose a path that will eventually lead to overcoming weaknesses in character. MacBeth's wife, Lady MacBeth, is a tragic character in her own right who becomes insane shortly after she and MacBeth murder King Duncan.