It's very simple. When you drive the car the compression of the tire during each revolution increases the temperature of the air in the tire. Considering the air in the tire to be an ideal gas, the relationship between temperature, pressure and volume for a fixed amount of mass $m$ of air in the tire is given by

$$PV=mRT$$

Where $R$ is the specific gas constant for air. Now, assuming the volume of the tire does not change appreciably, if the temperature goes up the pressure goes up proportionally.

Hope this helps.

It's very simple. When you drive the car the the tires heat up due to rolling friction. This increases the temperature of the air in the tires. Considering the air in the tire to be an ideal gas, the relationship between temperature, pressure and volume for a fixed amount of mass $m$ of air in the tire is given by

$$PV=mRT$$

Where $R$ is the specific gas constant for air. Now, assuming the volume of the tire does not change appreciably, if the temperature goes up the pressure goes up proportionally.

Hope this helps.