Servo-assisted pilot solenoids:

This principle uses a direct-acting plunger valve as the pilot valve and a flexible diaphragm as the seal for the main seat.  As soon as the pilot valve opens, the fluid chamber above the diaphragm is discharged.  The media pressure within the diaphragm raises the diaphragm and opens the valve so that the medium can flow.  If the pilot valve is closed, the media pressure above the diaphragm builds up again through the small pilot tube/hole opening and the closing process is assisted by the closing spring.  Minimal differential pressure between the inlet and outlet is necessary for complete opening and closing.

Application:
The main uses for these valves are clean liquid or gaseous media such as compressed air, water, hydraulic oils, etc.  The small pilot valve makes them less expensive than direct-acting valves for use with higher pressures and larger diameters.
Since pilot-controlled valves (also: servo-assisted valves) have only a small pressure equalisation hole in the diaphragm, up steam strainer is recommended.  Coil voltages are lower than direct acting due to less force needed to open the valve.