Little is known about this one, because Kowalski brings it up at the beginning after talking about how much he likes the MMU prototype, stating that he prefers his '67 Corvette. Kowalski asks if he ever told Mission Control the Corvette story, only to be rebuffed by Houston, who tells him that they know the story, espescially in Engineering.
All that is known about the Corvette story is that Kowalski's car was from 1967 and that the Engineering department had heard it more times than Mission Control.
A Corvette is a sports car designed for racing that is equipped with a supercharged V8 engine that is capable of traveling at speeds of well over 230 miles per hour. They are expensive, but nonetheless some of the most popular cars ever made, still being produced today.