The Turbofan engine is essentially a turbojet engine. The only difference is that the turbofan has a large compressor fan to compress a lareger amount of air. Until the 1980s, the turbofan was essentially a engine for passenger planes and similarly large aircrafts, due to its better fuel efficiency. However, with improved technology, the turbofan has been incorporated on smaller jet fighters too! This has not only helped giving new planes greater range, but also the ability to super-cruise in some cases.
The engine is otherwise made to run like a conventional turbojet, where the exhaust forces the rear turbine blades to turn, which in turn moves the common shaft for the compressor fan blades and the ignition chamber.