Oedipus's act of blinding himself symbolically represents his ignorant decision to dismiss Teiresias's intimate knowledge of his past, by purposefully overlooking his message and the signs which reveal that he murdered his father and married his mother. When Oedipus is exposed to the truth, he is overcome with shame, grief, and remorse. Once Oedipus realizes that he was not able to avoid the prophecy and is responsible for the plague, he is disgusted with himself and stabs his own eyes using Jocasta's golden brooches.

Oedipus blinding himself reflects his emotional pain and reveals that he has taken responsibility for his actions. Oedipus acknowledges that his hubris has left him blind to the truth and is too ashamed of himself to witness the citizens' reactions. Overall, Oedipus chooses stab out his eyes as a way of punishing himself for his hubris and ignorance. His loss of eyesight also symbolically represents his previous decision to overlook Teiresias's message and ignore the truth. 

Broadly speaking, there are two reasons behind Oedipus' actions. First of all, the literal act of blinding makes explicit the metaphorical blindness that Oedipus has displayed throughout the play, and indeed throughout his whole life. To see Oedipus in such an appalling state, blood pouring down his screaming, eyeless face, really brings home to us the terrible price that Oedipus has paid for his overweening pride.

The second reason is more practical. Oedipus doesn't want to see the looks of pity, loathing, or contempt etched on the faces of people who now know the terrible truth. It is a great source of shame for Oedipus that he killed his father and married his mother, albeit inadvertently. He literally cannot look other people in the eye now that the truth has finally been revealed.

Oedipus' decision to blind himself is very symbolic.  Because of his hubris, he was blind to all of the warning signs about the path he was travelling.  He refused to see.  In the end, when all is brough to light, he blinds himself, so he finishes the play literally as blind as he figuratively was throughout.

He is unable to avoid the fate that had been foretold for him from his birth.  He also brings curses upon himself, by cursing the murderer of Laius.  His self-punishment reveals that he believes his suffering is deserved.  It is his attempt to bring justice to the situation.