There are various methods of cleaning the engine, most using water or a mixture of water and a detergent.
I have seen the use of a water/Magnus solvent (Magnus is a trade name but most of us call this stuff "Magnusol") which is quite a powerful degreaser. The mixture is sprayed into the intake while the engine is dry-motored then pure water is sprayed to rinse. The Magnusol is normally clear but turns white on contact with water, so its quite easy to determine when the engine is completely rinsed.
Magnusol is quite corrosive if you don't rinse thourougly.
The walnut shell method is often called a carbo-blast. It is effective and creates a great light show but the abrasive qualities of the material cause some erosion of the blades so its not used anymore as far as I know. Of course someone out there will come up with proof of someone in darkest Africa still using this method!
The ground-up walnut shells are fed into a hopper that releases them into the running engine.
The benefit of engine cleaning is purely one of maintaining efficient blade shape. Each compressor and turbine blade are tiny airfoils whose shape is ooptinmized for their purpose. Grime and dirt that builds up, modifies the shape of the blades not unlike icing on the leading edge of a wing and spoils the efficiency.