Your car has to fight against friction to maintain its motion. There are two categories of friction: internal friction in the engine, the transmission and every other component where moving parts are found and external friction. Here is a breakdown of engine friction by subsystem. The external friction comes from rolling resistance in the tires and air drag.
The resistance of the tires depends primarily on the contact area with the road. Minimizing this area minimizes friction. In the picture you can see than underinflated tires have flat, square contact areas. The outer edges of the tires touch the road. Correctly inflated tires will not touch the road with the outer edges. Overinflated tires will have even less contact area and less friction but they will give you a bad, bumpy ride. It is even possible to damage the undercarriage of your vehicle with overinflated tires because they will not be helping to soak up shock and vibration.
The air resistance depends on the shape of your vehicle and the speed you are going. At low speeds the air resistance is low and increases slowly. At higher speeds the air resistance is large and increases rapidly. Low speed driving is dominated by tire resistance and high speed driving by air resistance. The tire resistance is constant, basically independent of speed. The chart above compares the tire and air resistance and shows their total.
Knowing the relative contributions of tires and aerodynamics helps understand what is happening. For example, there is a debate about whether running the air conditioner or opening the windows (and thus increasing air drag) is better for gas mileage. Since the open windows add to air resistance which is small at low speeds, we can tell that for low speeds windows down and air conditioner off saves on gas.