The extremely hot, high pressure air rushes by the turbine blades making them spin at a high rate of speed. The turbine blades are connected back to the compressor blades by a shaft. The turbine blades take some of the energy from the air and returns the energy to the compressor. This moves the engine forward. To increase the thrust, a device called an afterburner is sometimes built into the engine.
Fuel is dumped into the hot exhaust gas coming out of the nozzle.
This causes another controlled explosion. This makes the air even hotter which adds more energy to it. This increases the thrust. This is not an energy efficient method. So it is used only for brief periods when extra thrust is needed.