The concept of a jet engine is basically a rocket that uses air as the oxidizer instead of something that's already stored on board. There are many types of jet engines, but I will focus on turbojets. The purpose of a turbojet is to push a lot of air out the back of itself at high speed to provide forward thrust. It does this by combining the air with a fuel like propane or kerosene in a combustion chamber and igniting it to cause it to expand and rush out the rear of the engine. The heated, high pressure gasses flowing out spin a turbine at the back of the engine which provides the power for the compressor. The compressor is a fan at the front of the engine that forces air into the combustion chamber to be mixed with fuel.
This instructable will show you how to build a small turbojet from scratch. This design could be scaled up to be used on anything once you have practiced with a small one.