A turbojet is a kind of jet engine that works by squeezing air into a small space, mixing it with fuel, and setting it on fire. The mixture of fuel and air goes out the back of the engine and pushes it forward. As it leaves the engine it spins a fan which turns another fan at the front which sucks in more air.
Turbofan engines are more complex, and more common today because they can make more power for the same amount of fuel than a turbojet, they also make less noise. Supersonic aircraft still use the simpler kind.