According to Liddell and Scott's Greek-English Lexicon, the noun peripeteia refers to a turn in the opposite direction, a "reversal", a "sudden change", or, among other definitions, a "sudden reversal of circumstances."
With respect to Sophocles' play, the term peripeteia became famous because Aristotle, in the Poetics (see 1452a22), used it to describe the reversal that occurred when the messenger from Corinth came to tell Oedipus that Polybus had died. After Oedipus told the Corinthian about the dreadful oracle, the messenger thought that he could relieve Oedipus of his fears by telling him that Polybus was not actually his father.
My lord, since I came to make you happy,
why don’t I relieve you of this fear? (Ian Johnston translation)
When Oedipus hears this news, though, he soon experiences, according to Aristotle, peripeteia. Upon learning that Polybus and Merope were not his real father and mother, Oedipus soon discovers that Laius and Jocasta were his parents. This discovery, of course, leads to Jocasta's suicide and Oedipus blinding himself.
Ah, so it all came true. It’s so clear now.
O light, let me look at you one final time,
a man who stands revealed as cursed by birth,
cursed by my own family, and cursed
by murder where I should not kill.