The turbopump is the heart of most liquid-fueled rocket engines.
Gas generator engines tap off and burn a little propellant to drive a turbine, which turns a centrifugal pump, which rapidly pushes the fuel and oxidizer to the combustion chamber, after the cryogenic fuel first circulates around the rocket nozzle to cool it. The combustion generates supersonic exhaust out the converging-diverging nozzle that pushes the rocket. (The nozzle pushes the exhaust, and the exhaust pushes the nozzle).
The Merlin is an open-cycle engine because the fuel-rich flow of its gas generator is dumped overboard and not fully burned in the combustion chamber. The Raptor is a closed-cycle and full-flow staged-combustion engine as all of its propellants flow through the pre-burners (aka gas generators) to fully burn in the combustion chamber in the optimal ratio and exhaust out the nozzle for maximum efficiency.