You don't need parking lights to park in your driveway or practice parallel parking or drive through the park. So when do you use parking lights? Like many subjects, the life and times of parking lights can only be properly understood by starting at the very beginning of their history.
TL;DR (Too Long; Didn't Read)
If a modern car has parking lights, they are next to and connected to the headlights and used to help other drivers see the vehicle.
The Heyday of Parking Lights
Parking lights are lights attached to the outside of headlights, sometimes with a similar set in back. Today, they are not nearly as important as they were in their heyday, when they were known as "sidelights" and played an essential role in protecting the vehicle.
Parking lights (sidelights) used run on a different operating system than the headlights so that they were available even when the headlights failed. Drivers used parking lights when they had to park their cars at night on narrow, poorly illuminated roads. Their purpose was to alert other drivers to the fact that a car was parked there. In most countries, parking lights must be bright white, but in the United States they are often amber or gold to make them look different from brake lights (red) and headlights (white).
Over the years, the use of parking lights has diminished. Roads became wider and better lit. And, most cars have emergency flashers or hazard lights to warn drivers that a car is parked on a roadside. Headlights are brighter than they were and do a better job of illuminating a car's location than parking lights. Starting in 1968, parking lights have been attached to the same wiring system as headlights. They illuminate at the same time as the headlights as an additional means of lighting up a vehicle.
Purpose of Parking Lights Today
Parking lights are not required by state or federal law today, but a lot of new cars still have them. Manufacturers say that the purpose of parking lights is to make cars more visible from the side.
This seems a bit of a stretch, especially when so many new cars come with "daytime running lights" that illuminate whenever the engine is running, ensuring that the car will always be visible to other drivers. However, parking lights can be extremely useful as backup lights in emergencies.
For example, let's say one of your headlights burns out and you are on a back road, far from home. The parking light will shed some light on that side of the car. The risk in that situation is that your car will be mistaken for a motorcycle, and the parking light glow will confirm to other drivers that you are in fact a car and require a full lane.