Plain English Meaning
A system that uses moving air to make certain instruments and parts work. On most small airplanes, it's what spins the gyros inside the attitude and heading indicators so they can show the pilot which way the airplane is pointing and tilting.
Full Definition
An aircraft system that uses compressed air to power instruments, components, or controls. In light aircraft, the pneumatic system most commonly drives gyroscopic flight instruments such as the attitude indicator and heading indicator, using either an engine-driven vacuum pump that pulls air through the instruments or a pressure pump that pushes filtered air through them.