When it comes to serious power-adders there's two main contenders: twin turbos and superchargers. While the two are very different there are some similarities.
The main similarity between twin turbos and a supercharger is that they both force air into the motor in order to create more power. To put it simply, the more air forced into your motor, the more power it will make.
A supercharger is a unit that bolts on to the motor and is connected by a belt. The engine’s pulley spins the belt which spins the supercharger forcing air into the motor. The smaller the pulley the faster the engine spins the supercharger which means more air getting pushed into the motor. You can read more about the different types of superchargers and how they work here. The limit to superchargers is their efficiency. Superchargers use horsepower to make horsepower and if you overboost the supercharger, the air being forced into the motor will be hot which results in a loss of power. We call this heat soaking and it can be avoided with a chill box.
Turbos are similar to superchargers in that their main goal is to also force as much air into the motor as possible. However, turbos use your engine’s exhaust gases to spin the turbine rather than using the engine itself. This makes turbos more efficient than superchargers because you’re not using horsepower to create horsepower. Instead, your engine is using it’s bi-product, the exhaust gases, to make power. Turbos are also able to spin much faster than superchargers. However, when you're racing you have to allow the turbos to spool. They need a little bit of time to build boost. Superchargers build boost simultaneously because it uses horsepower to make power. Turbos use the bi-product of the motor to make power so you're waiting for those exhaust gases to be created in order to spin the turbines.
Both turbos and superchargers have their pros and cons. Turbos make more horsepower and run more efficiently but they’re typically more expensive and the installation isn’t as clear-cut compared to a supercharger. Superchargers can be put on your daily driver rather easily and with the right set up, it can be a 9-second car.