A diffuser, in an automotive context, is a shaped section of the car underbody which improves the car's aerodynamic properties by enhancing the transition between the high-velocity airflow underneath the car and the much slower freestream airflow of the ambient atmosphere. It works by providing a space for the underbody airflow to decelerate and expand so that the boundary between the car's airflow and "external" airflow is less turbulent. It also provides a degree of "wake infill" (the wake being a turbulent area of low pressure that is caused by the passage of the vehicle through the air; this can cause pressure drag).
As the air enters towards the front of the car it accelerates and reduces pressure. There is a second suction peak at the transition of the flat bottom and diffuser. The diffuser then eases this high velocity air back to normal velocity and also helps fill in the area behind the car making the whole underbody a more efficient downforce producing device by reducing drag on the car and increasing downforce.
The aft part of a car underbody can be a diffuser. It works to bring the low pressure air below the car back to the ambient atmospheric pressure without inducing turbulence. It uses Bernoulli's principle, such that the pressure increases while the velocity decreases. Since the pressure below the car is lower than on the side and above the car, downforce is produced if implemented correctly. Injecting the exhaust into the rear diffuser can also help extract the air from below the car. The exhaust gasses effectively energize the boundary layer, helping to raise the pressure of the low-pressure, fast-moving airstream back to the ambient atmospheric pressure at the exit of the diffuser. This helps extract the air more efficiently from the underbody.
Note that the front of the car slows down the air without a diffuser making this the ideal place for an inlet. Instead, a splitter is commonly used here. The splitter serves to reduce the pressure below the front of the car and thereby increase the amount of downforce in that region. The airstream is brought to stagnation above the splitter, by an air dam, causing an area of high pressure. Below the splitter, air is accelerated, as stated above, which causes the pressure to drop and create downforce. Some race cars, such as the Toyota GT-One actually use a proper diffuser in this area to help create more downforce.