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The quality parameter like Rarity is basically a measure of how rare or unique a car is. This can affect a few different things about the car.
Firstly, it affects the attributes of the car. Attributes are things like Performance, Wear and Tear, Eco-Friendliness, Fuel Economy, and Fuel Tank Capacity - basically all the different qualities that make a car good for driving and gaming. When a car is created (or "minted"), the points for each attribute are set randomly within a certain range based on the car's rarity. So, a rarer car might have better attribute points than a more common one.
Secondly, rarity affects the car's fuel or energy supply. This is basically how much fuel or energy the car has to use during a race. Again, rarer cars might have more fuel or energy than more common ones.
Finally, rarity affects the cost of the car. This probably makes sense - if a car is very rare and has really good attributes and energy supply, it's going to be worth more money.