If you have a car with a rear-wheel drivetrain, then you have what's called a live axle. That means your wheels are connected to the axles via bearings, and the power from your engine is transmitted to the wheels through these axles. Your ring and pinion gears are located in the differential, which is a gearbox that sits between your live axles. The ring gear is attached to the differential case, while the pinion gear is meshed with it and connected to your driveshaft.
The ratio between these two gears determines how much torque is transferred from your engine to your wheels. A higher ratio (a taller gear) will result in more torque being transferred, but less speed. A lower ratio (a shorter gear) will do the opposite - less torque but more speed. So if you're looking for more power/acceleration, you'll want to adjust your ring and pinion gears to give you a taller ratio. Conversely, if you're looking for better fuel economy or top speed, then you'll want a shorter ratio.
There are three main ways to adjust your ring and pinion gears: changing the size of either gear