Oedipus Rex or Oedipus the King recounts the story of Antigone's father, Oedipus. There is a longer story, but the short summary is this: Oedipus has become the king of Thebes by solving a riddle and ridding the town of the Sphinx which has been plaguing the city. His "reward" is getting to marry the queen, Jocasta. When the play opens, the city is literally dying, as from a curse--babies and crops and animals, none of them are flourishing. As a concerned king, Oedipus sends for the gods to reveal the cause of the curse under which Thebes is suffering. Once he knows the cause, his intent is, of course, to eliminate the curse so his city can once again thrive. The gods send the blind prophet, Teiresias, to deliver the news that Oedipus himself is the curse. He is not believed, and Oedipus treats the prophet horribly and sends him on his way. Shortly thereafter, his brother-in-law Creon also arrives with a message from the gods stating essentially the same thing--Oedipus is the source of the curse and he must leave Thebes in order for it to flourish. The haughty Oedipus does not believe him, either, accusing him of trying to usurp the throne. Soon, though, the truth is revealed: Oedipus is discovered to have killed his father, Lauis, and married his mother, Jocasta, just as the gods had predicted and despite Oedipus' attempts to thwart their predictions for him. His wife/mother immediately commits suicide and Oedipus violently blinds himself as he understands the horrific nature of his crimes and the consequences he has brought upon the city he loves. Oedipus asks to see his children/brothers and sisters one last time (though all he can do is touch their faces), asks his brother-in-law/uncle to take care especially of his two daughters (Ismene and Antigone), then asks to be banished to the hills. All his requests are granted.
On a personal note, I'm sure you're reading Antigone for class, but I'd encourage you to also read Oedipus when you're able. There is more depth and irony than I've shared here. and it's actually a delightful read. I've also included a very good e-notes summary of Oedipus below.