A short definition of the word hubris is generally presented in two words: excessive pride. In the literary world and the world of the Greeks, this was also true but had one added element. This overblown pride was the very thing that caused the character's downfall. So hubris might be defined as excessive pride which causes one to fall from a high place, often taking others down, as well. Of course this is exactly what happens to both Oedipus and Jocasta in Oedipus Rex by Sophocles, and neither of them can blame anyone other than themselves.
Jocasta's two primary displays of hubris are connected and are also the cause of her eventual shame and death. First, we learn that Jocasta and Laius received an awful prophecy about their son: he would one day kill Laius and marry Jocasta. Of course this is unacceptable to the couple and Jocasta cruelly sends her son away to die a painful death in an effort to thwart the plans of the gods. Of course thinking that one can outwit the gods is the supreme pride, for it assumes that she and Laius are more powerful than the gods. What she does not know, of course, is that her son did not die and the prophecies did, in fact, come true.
Her second display of hubris comes late in the play when she brags to everyone that she managed to outwit the gods with this act and therefore gives no credence to anything the gods or oracles have to say. This is the same kind of arrogance, and she does it publicly. She dismisses the words of the prophets (human spokesmen for the gods), saying:
All right, forget about those things you’ve said.
Listen to me, and ease your mind with this—
no human being has skill in prophecy.
She is clear that the gods may do what they will but prophecies made by oracles are worthless. Jocasta did the very thing she was certain could never happen; she married her son. When this relationship becomes known, she is ashamed and commits suicide. Her pride caused her fall.
Oedipus does the same thing. When he is told by the oracle that he will marry his mother and kill his father, he arrogantly thinks he can outrun his fate. He does both of those things, though he does not know it, and is elevated to king because of it. This mighty rise foreshadows a mighty fall when all is revealed. The first lines he speaks reveal his arrogance:
Here I am – myself – you all know me, the world knows my fame: I am Oedipus.
The theme continues when he later determines that he will do what the gods have not revealed; he will find out who murdered Laius:
I’ll start again – I’ll bring it all to light myself!
The great irony of Oedipus's hubris is that he literally determines what his fall will look like. When he arrogantly proclaims that he will curse the man who brought all this trouble on Thebes by killing Laius, he is cursing himself.
And on the murderer this curse I lay
(On him and all the partners in his guilt):--
Wretch, may he pine in utter wretchedness!
And for myself, if with my privity
He gain admittance to my hearth, I pray
The curse I laid on others fall on me.
See that ye give effect to all my hest,
For my sake and the god's and for our land,
A desert blasted by the wrath of heaven.
Again, Oedipus believed he could challenge the gods and outmaneuver fate, but of course that very arrogance put him in the position of fulfilling the prophecy and then being punished for doing so. It is ironic that both Oedipus and his mother displayed the same kind of excessive pride and both fell because of it.