How do jet engines work?
In the simplest of terms:


Suck - Air is sucked into the turbine. For efficiency reasons, most aircraft let some of that just pass through the outer part of the fan, rather than through the whole engine.
Squeeze - The compressor squeezes that air together to a high pressure. This helps with ignition.
Boom - Fuel is injected and ignited. As the air gets hot, it expands.
Blow - The hot air drives the low-pressure turbine (driving the whole shaft holding the engine together), sucking new air in, and is itself blown out the back.