What does "tyrannos" mean in the play Oedipus Rex?
In our culture, we might see "tyrannos" and think "tyrant" which refers to a leader (e.g., a king) who is a cruel and unjust leader. He rules by force, through fear, without benefit of a democracy. Tyrants are often seen as murdering rulers who take power and sustain it through excessively harsh means.
However, during the time of the early Greeks (and Oedipus was written by Sophocles, a Greek), "tyrannos" could refer to anyone who came to rule through "unconventional" means. The ruler was not necessarily one who was harsh or cruel, but who simply gained his power in an unusual way.
Wikipedia.org provides the association of the word in the early Greek culture:
In ancient Greece, tyrants were influential opportunists that came to power by securing the support of different factions of a deme. The word "tyrannos" then carried no ethical censure; it simply referred to anyone, good or bad, who obtained executive power in a polis by unconventional means.
Therefore, "tyrannos" does not indicate that Oedipus was a harsh or unjust ruler: the story shows that he was a just man. His guilt over what he has unknowingly done causes him to blind himself and leave the throne and his kingdom. "Tyrannos" indicates that Oedipus came to the throne in an unusual way.