The purpose of tragedy, according to Aristotle, is to produce pity and fear in the audience. Pity that a person so great could fall so far, and fear that we could meet the same end if we are not careful. In order to tragedy to have this effect, a certain type of character is needed.
For Aristotle, a tragic hero (the protagonist of a tragedy) needs to be an understandable, realistic character. Aristotle felt that drama should be an imitation of reality, and therefore the characters needed to be types that could exist in our world. The tragic hero was typical noble and upright, behaving appropriately for his/her situation and overall well-liked. However, the hero had a major character flaw (hamartia) which brings about his/her tragic end (typically death, especially in Shakespearean tragedy). If the character wasn't believable, the catharsis of the tragedy would not be achieved. According to Poetics, these character traits should be revealed through indirect characterization -- through the actions of the protagonist and his/her interactions with others.