The airwash system can vary from manufacturer to manufacturer.
A stove with an airwash system will tend to have a cleaner window. In non airwash stoves as tar is deposited on the window when fuel is burnt (especially wood) darkening the stove glass or making it black. Airwash stoves take in air from above the stove window and pass (or ‘wash’) it over the surface of the window. This helps keep the flames and gasses in the stove off the window itself as there is a layer of air protecting it. Less tar is deposited keeping the window cleaner.
This video from Jotul helps to explain how it works.