A birth defect was any physical malformation present since or before birth.
In 2367, while posing as Rivas Jakara, William T. Riker claimed to Berel that the reason his cranial lobes appeared to be surgical implants was because he had undergone cosmetic surgery to correct a birth defect. He also explained the appearance of his hands the same way, claiming that his father's were the same way. (TNG: "First Contact")
In 2377, The Doctor believed that a birth defect was reponsible for Iko's violent behavior. This defect was inadvertently corrected when the Doctor applied some of Seven of Nine's Borg nanoprobes to the Nygean in order to heal his physical injuries. (VOY: "Repentance")