A system that uses air to power something.
For instance, have you seen the tube systems at bank drive-up tellers? Air is used to push the tubes back and forth from the teller to the customer.
Air is also used to power drills, sanders, grinders, and the like at garages and car body shops.
Additionally, you can find pneumatic systems in large buildings or complexes. They're used there to control the air handling systems, the HVAC. Control systems decide which system valves to actuate and they are operated by pneumatics.