A turbocharger is hooked up to the exhaust system. The exhaust heat and pressure spins a turbine which acts like an air compressor and pushes air into the intake. The additional air will add more fuel into the engine and thus the combustion inside the engine will be bigger and the engine will spin faster and push the car faster. All the heat and pressure inside the turbocharger is controlled by the addition of a wastegate which looks similar to an exhaust pipe coming out of the engine. Synthetic oil, frequent oil changes and the extra time of idling a few minutes before turning off the car are a few extra steps required for turbocharged cars.
Superchargers do the same thing as a turbocharger but instead of being powered by the exhaust it is being spun by a belt attached to the engine’s crankshaft so the faster the engine is turning the more air the supercharger puts out. Superchargers also get very hot and need intercoolers and aftercoolers to regulate the temperature.
A car can have both of these systems in it since they are in different locations and cars can also have twin turbo meaning they have two turbochargers in them.