A chick who goes out with a guy ONLY for the benefit of his nice vehicle; usually a nice shiny jacked-up 4X4 truck with oversized tires, or even a hot sports car. Hence the name, "tire-biter."
Conversely, it CAN refer to a guy who goes with a girl solely for HER nice wheels.
That gal is a total tire-biter, she only wants him for his truck.