Talking about road branch, tire pressure seems to be one of the most important adjustments for our performance on track, but it has been always one of the most confusing issues.
Due to the continuous improvement (and change) of the NTM (New Tire Model) every season are susceptible to change. It is better to have some basic knowledge about what the pressure does and make our own adjustments.
Under-inflated: Wears the edges of the tread more than the center. Gives us more grip after some laps, but it is more aggressive with the tires and finally wears more than a proper pressure.
Over-inflated: Wears the center of the tread more than the edges. Gives us more grip in the first laps suffering a cliff afterwards. More top speed.
Proper: The entire tread is worn at the same rate (aka, correct pressure). It should be the perfect balance between outer and inner temperatures of the tread. It takes 2-3 laps to get a consistent grip.
Getting the proper pressure on our tires will allow us to get more from our car.
Until my knowledge, higher pressures are usually used in the qualifying sessions to get a good temperature as fast as possible. Lower pressures are more suitable to be used in race sessions where the grip and the progress of the tire development is a more important fact to maintain our time laps.
Playing with the different ride heights and the pressure in the front and the rear we can affect substantially how the car behaves. Lower pressure in any of the axis of the car will cause more grip on that axis.
Front lower pressure: More oversteer.
Rear lower pressure: More understeer.
In road, use symmetric pressures on both sides to stabilize the behavior in different kind of corners.
These are some basic advice for the tires, at least to begin to understand how to tune our car.