Car Masteries are perks you can apply to each car you own. Each one improves your gameplay experience in some way while you drive that car, such as earning extra Influence while you race, giving you a free Wheelspin etc.
Each car has its own skill tree, with some cars having more Car Masteries to unlock than others.
Car Masteries are unlocked by spending Skill Points on a car; this is done through the [Cars] menu when you pause the game.
Choose any car, earn a Skill Point (for driving around the game world and earning Skills) and spend it to unlock the Achievement.