Rockets rely on incredibly powerful chemical reaction engines. SpacePod explains in detail exactly how rocket engines work.
A chemical rocket uses a fuel source and an oxidizer. There are three primary things that make up a rocket engine, and with it, rocket fire: the combustion chamber, the throat, and the nozzle. The combustion chamber is where the fuel and the oxidizer first begin to mix. The throat is where the high pressure but slow gases of the combustion chamber are converted into low pressure but very fast gases that come out of the nozzle. Thus, thrust is created. The massive acceleration of the fuel’s transformation from liquid to gas is what causes the momentum.