Character Analysis
Theseus—often called “child of Aegeus” because he's, well, the child of Aegeus—is the ruler of Athens, which includes Colonus, the sacred grove where Oedipus has come to die. He’s a pretty reasonable guy overall, and because of his reasonable response to the cursed wanderer taking up residence in his town he gains an awesome good-luck charm: Oedipus’ grave.
The king knows that Oedipus is bad news; the Chorus wants to kick Oedipus out. But Theseus is also a pious man—every time he comes he’s getting called away from making sacrifices to Poseidon, the god of the sea. This behavior shows that he’s in good with the gods, so he wouldn’t want to go against them like Oedipus did.
Theseus realizes that he’s no better than Oedipus because Oedipus didn’t know what he was doing when he committed his crimes. He says to him:
So there is no stranger, such as you are now,
From whom I would turn aside or refuse to save. Since
I know well, being a man, that I have of tomorrow
No greater share than you have. (565-68)
Theseus has been in Oedipus’ shoes. That’s why he’s willing to give the poor guy a chance.
Well, that, and the offering that Oedipus promises him. The king is driven not only by his rationality, but also by a desire to protect his kingdom:
Then, he has come as a suppliant of the deities, and
Pays no small tribute to this land and to me.
These things inspire my reverence, and I will never cast out the favor
Of this man, but on the contrary, I will settle him in my land. (634-37)
If Oedipus’ grave can protect Athens, then Theseus is willing to protect Oedipus in order to keep the body on Athens’ soil. He’s a king for his country.