Modern turbofans evolved from the 2-spool axial-flow turbojet engine, essentially by increasing the relative size of the Low Pressure (LP) Compressor to the point where some (if not most) of the air exiting the unit actually bypasses the core (or gas-generator) stream, passing through the main combustor. This bypass air either expands through a separate propelling nozzle, or is mixed with the hot gases leaving the Low Pressure (LP) Turbine, before expanding through a Mixed Stream Propelling Nozzle. Owing to a lower jet velocity, a modern civil turbofan is quieter than the equivalent turbojet.
Depending on specific thrust, ducted fans operate best from about 400 to 2000 km/h (250 to 1300 mph), which is why turbofans are the most common type of engine for aviation use today in airliners as well as subsonic/supersonic military fighter and trainer aircraft. It should be noted, however, that turbofans use extensive ducting to force incoming air to subsonic velocities (thus reducing shock waves throughout the engine).
How a turbofan engine works