Car classes are a “ranking” of performance based Car Attibutes upon power, handling, acceleration and braking.
Above is an example of a Class B race. This means the car must be a Class B vehicle. Upgrades may push a car beyond class B so carefully add and tweak a car with handicaps to utilize it and maintain the class you desire.
Class Reference Guide
At anytime, you can view an up-to-date class guide Community/Guide→Car Classes section on Andatura 4. The specific cars change as cars are added to the game.