The majority of planes use jet engines to propel themselves. Air is drawn into the rotating compressor via the intake and is compressed to a higher pressure before entering the combustion chamber. In a fascinating way the compressed air is mixed with fuel and ignited by a flame. This combustion technique considerably raises the temperature of the gas. The chemicals created from the combustion exits the combustor through the turbine where the energy comes from to employ the compressor. Even though this expansion process reduces both the gas temperature and pressure at exit from the turbine, both variabels are mostly still well above ambient conditions. The gas stream exiting the turbine expands to ambient pressure through the propelling nozzle, causing a high velocity jet in the exhaust plume. So if the jet velocity surpasses the aircraft flight speed it amazingly creates a forward thrust.
Primarily, the pumping action of the compressor prevents any backflow, this kindly helps the flow of the jet engine. You can compare the whole method with a four stroke cycle, but with induction, compression, ignition, expansion and exhaust taking place simultaneously. How efficient a jet engine is depends on the pressure ratio (Combustor Entry Pressure/Intake Delivery Pressure) and of course the cycle turbine inlet temperature.
We can also try to compare a turbo jet engine with a propeller engine. Turbojet engines take a fairly small mass of air and accelerate it by a large amount, whereas a propeller takes a large mass of air and accelerates it by a small amount. At great speed the exhaust of a jet engine makes it efficient at high speeds (particularly supersonic speeds) and high altitudes. On slower aircraft and those required to fly short stages, a propeller powered by a gas turbine, well known as a turboprop, is far more common and also more efficient. Especially small aircraft primarily use common piston engines to drive a propeller but small turboprops are getting smaller as engineering technology improves.
The above described jet engine is what people call a single spool design, which means that the turbine is connected to the compressor by a single shaft. Higher Overall Pressure Ratio designs often have two concentric shafts, this is to severly improve the stability of the compressor during engine throttle movements. Essentially it's the outer shaft that connects the turbine engine to the high pressure compressor. The combustor together with the high pressure compressor spool forms the gas generator of the turbine engine. We must not forget that the inner shaft connects the low pressure compressor to the low pressure turbine to ultimately create the low pressure spool. This incredible piece of technology allows both spools to operate at their own optimum shaft speeds.