What is the difference between a Gas turbine engine and a piston engine?

a compressor does work on the gas , raising its pressure and temperature

a turbine does the reverse , it expands the gas as it passes through the turbine, extracting energy from the gas to do mechanical work.

For a typical jet engine , the flow track on a compressor is of a converging cross section while is it diverging for the turbine, which is as per gas dynamic laws.

The Turbine does two things here in the jet engine, one ,it runs the compressor and two, expands the gas to the propelling nozzle which produces thrust by accelerating the gas upto its exit.