Oedipus, after discovering the truth of his own identity and how he was the one who killed his father, and therefore brought the plague upon the city of Thebes, wishes for oblivion, or complete forgetfulness to descend upon him so he doesn't have to face the tragedy of realising who he is and what he has done. Note how he clarifies what he means by "oblivion" in the following quote:
No, if I could just block off my ears, the springs of hearing, I would stop at nothing--
I'd wall up my loathsome body like a prison,
blind to the sound of life, not just the sight.
Oblivion--what a blessing...
for the mind to dwell a world away from pain.
For Oedipus, in the midst of the pain and shock he faces when he confronts who he is and what he has become, oblivion can only be seen as a "blessing" because it would give him separation from the terrible pain he faces. For Oedipus, oblivion is the only possible way in which he can achieve some sort of peaceful existence, so terrible is the truth of his identity and what he has done. His desire to be exiled and sent out to wander far away from any other humans is really a blessing in disguise, as only then does he have any chance whatsoever of gaining some measure of peace in the silence he will enjoy, as opposed to the recriminations that his infamy will gain him wherever he goes.