OK, this answer will definitely be trumped by better ones, and Google will serve you better, but until then....
Thrust is basically throwing a mass of stuff in the opposite direction you want to move in. The more weight &/or speed you can throw it, then more thrust.
We want to throw air (because there's a lot of it around, and it's what we want to be thrusted about in).
You could produce a small amount of thrust if you just squirt highly compressed air or steam through a nozzle, perhaps from a storage cylinder; the greater the stored pressure or amount, the faster or more of the air escapes, the greater the thrust. You would need a vast amount of stored air to do this for any length of time.
So, a glorified deflating party balloon.
You could produce a small amount of thrust if you squirted a fuel, with enough air to burn, into a chamber with an opening at one end; the more burning fuel, the greater the expansion & the faster the hot gases escape through the opening, the greater the thrust.
But it would really just be a noisy barbecue.
You could combine these two things, using the compressed air to considerably increase the amount of fuel burnt in the chamber, increasing the thrust.
Then you'd have a very hot, very inefficient rocket engine.
However, if at a point just after the fuel has completely burnt in your chamber, you stick a fireproof windmill (turbine) into the flow of escaping gases, driven by this flow to turn a shaft and connect that shaft of the windmill back to a point where the air is coming from before it is mixed with the fuel, to a fan (compressor) that is turned by the shaft to drive the flow, then the faster the turbine is turned, the more air can be supplied by the compressor, to burn even more fuel, which in turn means the turbine is turned even faster, which turns the compressor faster so yet more air can be supplied, and so on.
So the burning fuel becomes expanding gases which accelerate the turbine, which powers the compressor, which allows more fuel to be burnt under higher pressure, to accelerate the turbine. The air can just come from the atmosphere in front of the inlet to the compressor, rather than having to be stored in a compressed form.
You could divert some of the air from the compressor (it's now compressed & can be plumbed like a fluid, going through tight turns & small holes) to form a cooling shield around the flame so you don't melt the walls of the chamber.
In fact, once this process get going properly (it is not self-supporting until quite a high rpm), the compressor can supply much more air than is needed by the fuel, and this can be used to cool parts of the engine & can be added to the exhaust as extra thrust.
So, starting at the air inlet, there's a compressor stage, then a combustion area, then a turbine stage, then the exhaust.
And you'd have a gas turbine engine. The combustion chamber is obviously vital to this process.
Gas turbines actually use a huge proportion of their energy just to keep this process supporting itself; what energy there is left over - just shooting out the back (turbojet) or driving additional turbines to turn fans (turbofan) or propellers (turboprop) or helicopter rotors or ships propellers or generators (turboshaft) - can still be considerable. The faster it goes, the more power.
Gas turbines have amazing power to weight ratio. You & three friends could manhandle a PT6A into the back of a station wagon; it produces the same power as a small rail locomotive. Unfortunately, gas turbines are not suited to constantly changing their power output like a car engine, and don't use that much less fuel when idling than when flat out.
It's an application of the Brayton Cycle; it's thermodynamics. It gives you a truly enormous increase in power because you can utilise the ability of stored fuel to create heat & expanding gas by burning it in really carefully controlled extreme conditions. In the combustion chamber.