Oedipus at Colonus is the middle play of Sophocles' Oedipus trilogy, and like a middle child, it's just not as smart or as pretty as the other two (kidding!).
After blinding himself, Oedipus left Thebes (or was he thrown out? It's unclear) and wandered the countryside, begging, for twenty years. Here's where Antigone earns her grit, and her suicidal rage: she goes with him and shares this life of poverty and deprivation. I gather from the reaction of the Elders of Colonus that he's persona non grata in most places because of the bad mojo he carries. "Do not pollute our city with your tainted air," and so on. Nice life for a growing girl.
Colonus is a holy site within Athens. Oedipus feels his death approaching and asks for sanctuary. He soon becomes a point of contention between Athens and Thebes, because the site of his grave will protect one from the other.
Oedipus seeks asylum from Theseus, ruler of Athens. Various important Thebans, including his brother-in-law Creon and his no-good son, come to try to kidnap him or convince him to come home. He refuses. He doesn't want to reward the relatives who turned him out when he was in need. Creon tries to take Antigone and Ismene with him by force, but Theseus prevents this and brings them back to their father. At the end of the play, Oedipus is dead and Polyneices, his son, is poised to attack Thebes with a foreign army, thus setting the scene for Antigone.
This conflict between Thebes and Athens over Oedipus is colored by subsequent history. Oedipus promises that the mercy Theseus shows him will result in a great benefit to Athens in the future. And in fact, according to my translation, 'Theban invaders were routed in a battle near the tomb of Oedipus.'
Antigone, who acted as his eyes, and Ismene, who loved him and tried to save him, are left alone in Athens. They decide to go back to Thebes and try to stop the war. But they will fail, and everybody will die.
I don't really understand why this play exists. I went browsing for commentaries and didn't learn much. Perhaps the most interesting bit of symbolism is the manner of Oedipus' death. Instead of being assumed into heaven, which is the current fashion is mysterious deaths, he is swallowed by the earth.