The air in tires can support a car because gases

Because the air inside the tires is kept at high pressure.

In fact, the force applied by the tires upwards to counter-balance the weight of the car (pushing downwards) is 

where p is the pressure of the air inside the tires and A is the area of contact between the tire and the car. Therefore, a higher pressure means a larger force F, and eventually if the pressure p is higher enough the force F will be large enough to counterbalance the weight of the car.