jet engines

[BubbaRoberts]

how do they work

[Top_Gooner]

have a look here

http://en.wikipedia.org/wiki/Jet_engines

[Clanad]

I couldn't open Top Gooner's link so if this is redundant... Just as in any fuel powered engine it's simply suck, squeeze, blow and go... Fuel is injected into highly compressed air and ignites on it's own (after initial spark assist) continously, which powers other turbine blades serving to power the front turbine blades, which compressed the air initially (technical name is N1). The gas then exits the rear of the engine with slightly higher ratio of compression than that which entered the front of the engine (ambient air). This difference is measured and presented on a gauge and is known as EPR. (Among pilots this is know as Eeper). This stands for exhaust pressure ratio. There's not actually not a lot of difference between the ambient air pressure nd that exiting the engine, but it's continous. For the most common aircraft turbine engine (Pratt and Whitney J2BD) it's only about 2.20 or so for take-off. Cruise power is usually at about 1.4 or so.
Some of the more modern turbine engines have variations on the theme but are essentially the same...

[Toureman]

To augment CLANAD's Excellent answer take a look at this, you can even start up the engine and take it up to maximum thrust, amazing.

http://www.geae.com/education/engines101/