Dikaiosyne - literally means justice in Ancient Greek; however there are several different interpretations as to what justice can mean. .
In The Oresteia by Aeschylus the definition of dike is the relationship between individuals. Justice becomes an issue of to what extent we are responsible for our actions and furthermore dike is seen as a correction of a wrong. In the Oresteia a complicated series of events plague the house of Atreus of Argos (Agamemnon, pg1) following the end of the Trojan War. Agamemnon returns from the war a hero, but upon his arrival he is murdered by his wife's lover and his cousin. However, the reasons for his murder are not simple. The murder is only a small part of a cycle of vengeance that began between the cousin's fathers. Aegisthus motivation for murdering Agamemnon was in retribution for the crimes committed against his father. As a result, Orestes, Agamemnon's remaining son, is now responsible for avenging his father's death. Orestes avenges the death by murdering his mother and Aegisthus for which he receives his mother's curse. Orestes is then plagued by the Furies for the murder. However, this poses the question of whether it is possible to end the cycle that this interpretation of dike establishes. A trial follows in Athens in which the cycle is finally ended with the help of Athena, the goddess of wisdom. Aeschylus, through the trial, is trying to say that the old cyclical system of revenge need not continue. In a democratic society with old laws and practices, there can be tribunal and judgment can be settled with wisdom (phronesis - wisdom along with justice will work). In addition his goal was to provide a functioning system of justice that does not involve the direct intervention of the gods.
Plato interprets dike as acting in accordance to one's station in life. Plato describes his concept of justice in terms of the allegory of the metals.