When Oedipus was three days old, his parents received a prophecy saying that he would one day kill his father. So, they pierced and bound his feet and sent him off to be abandoned on a mountainside. Oedipus survived the incident, but was left with scars on his feet. In fact, his name in Greek translates to "swollen foot."
Oedipus's scarred feet are more than a little symbolic. They highlight the fact that he has been marked for suffering from the moment of his birth. This expounds upon Sophocles's idea that humans have no power in face of the gods. For some mysterious reason, Oedipus has always been damned, and there's not much he can do about it.
The scars also highlight the irony of Oedipus's ignorance. Although his name blatantly points attention to his scarred feet (which are the keys to discovering his identity), Oedipus doesn’t realize his true identity until it’s too late. This one's on Jocasta as well. You'd think she might she might have clued in to Oedipus's name long ago and asked him how he got it.