A miracle worker was someone who could perform exceedingly difficult or unbelievable tasks with seemingly relative ease.
Montgomery Scott had the reputation of being a miracle worker. (TOS: "The Doomsday Machine"; Star Trek III: The Search for Spock, Star Trek IV: The Voyage Home; TNG: "Relics") In 1986, Leonard McCoy made the same claim about "Professor" Scott to Doctor Nichols. (Star Trek IV: The Voyage Home) Part of the reason he was known for his miracle working was allegedly due to his multiplying the estimated time it would take to effect repairs by a factor of four. He admitted as much after James T. Kirk, to whom he'd just promised to be able to complete a supposed eight week task in two, suggested he may have always done so, adding that he couldn't keep up a reputation for being a miracle worker if he didn't. (Star Trek III: The Search for Spock) He later advised USS Enterprise-D chief engineer Geordi La Forge that he had a lot to learn if he wanted people to consider him one, too. This comment was made after La Forge admitted he had been honest about how long a repair would take rather than exaggerating it. (TNG: "Relics")
In 2267, McCoy, while attempting to explain how "Lazarus"'s wound seemed to disappear, sarcastically described himself as "a bright young medic with a miraculous touch". (TOS: "The Alternative Factor")
In 2367, Bolian barber V'Sal teased La Forge, saying that although he realized the engineer wanted to look beautiful as a result of his ministrations, he was "just a barber, not a miracle worker", thereby calling La Forge ugly. (TNG: "Data's Day")