While studying the air-conditioning of the A320 from the FCOM I came across the information that the pack flow valves are "electrically controlled and pneumatically operated". I can not understand what it means.
It means that an electrical switching signal is used to drive the pneumatic or air valves in the air conditioning system.
Think about it like this: We want to use our garden hose to push open a cat flap but we want electricity to control the pressure in the hose. We could apply an electrical signal to a motor which opens the tap and lets water come out. This water pressure could then be used to control how wide the cat flap opens. The only difference in your airbus situation is that it isn't water (which would be hydraulics), it's air that comes out of the tap (Pneumatic means air). So this system would be called an electrically controlled, hydraulically operated system. Substitute the water in the hose for compressed air and you have your answer.
The way electrically operated valves work is generally based on the principles of electromagnetic force by utilising some sort of coil. This setup turns a piece of wire into an electromagnet, which is attached to or interacts with the movable part of the valve. This then ports air pressure to one side or the other, to balance open the valve to a set amount in proportion to the original electrical signal.
So we use electricity >>> this changes the balance of air >>> the air opens or closes the valve.
The valve can be fully open, fully closed or anywhere in between.
They're called "magnet valves". They're basically a valve that's operated by a solenoid.
Also seen on locomotive electrical contactors. The solenoid admits air, which moves an air piston which physically actuates the device. Doing that pure electrical would require gigantic solenoids, heavier wiring, heavier generator.
One thing to note is that unless your RAT generates compressed air, you lose your engines, you lose your air, and the electrical signal will no longer actuate it. I suppose on an A/C pack it hardly matters.