The faceplate switches provide a positive voltage to both segments of each individual valve. The trigger switch provides a ground to only one of those segments at a time.
For a valve soleniod to energize, both a positive and a ground voltage must be supplied. The diodes are to prevent unwanted backfeeding of signals.
Multiplexing is a way to add more handle functions without adding large quantities of extra buttons. Typically a faceplate switch will perform one function when the trigger is not pressed (i.e. extend cylinder #1), and a second function when the trigger is pressed (i.e retract cylinder #1).