Hydraulic proportional control valves work in a similar way to directional valves except they do not switch from fully shut to fully open. Instead, they gradually open a restricted flow orifice area. The size of the orifice opening is proportional to the amount the spool moves, either controlled by an electrical solenoid or a hand lever. In this image, you can see a directional spool switching (on top) and a proportional spool gradually opening (below). The proportional spool has a triangular notch that gradually opens a flow control orifice as it moves.
Flow is proportional to the amount that the valve orifice opens although the actual flow rate will also vary as the load or supply pressure changes. The shape and quality of the notch is also very important. Using a triangulated notch instead of a circular radius will provide a more linear flow vs opening characteristic.
It's useful to think of hydraulic control valves as a braking technology, rather than a driving one. They can be compared to a car's brakes rather than its engine. Valves, like brakes, are much smaller and control the vehicle's load by throttling or decelerating, rather than accelerating the vehicle, like an engine does.
Manually operated proportional valves
With a manually operated proportional valve you simply control the position of the spool with the position of the operating handle. Moving the spool increases the size of the notch opening and therefore reduces the size of the orifice restriction.
Mobile control blocks often use proportional pilot pressure control valves on the ends of the spools. These allows either electrical or hydraulic, remote pilot pressure control handles, to be located away from the proportional flow control valves.
Industrial proportional valves
Industrial proportional control valves more commonly use direct electrical actuation with PWM (pulse width modulated) power control to the solenoids. The electrical signal controls the force the coil exerts against the spring on the far end of the spool, and therefore the spool position and orifice size.
Accuracy is always a key issue with proportional control. In this graph, the cylinder position after the main deceleration phase would vary after each cycle. The creep phase is used to slowly bring the cylinder to a final limit switch before quickly decelerating to a more consistent stopping position.