Well a quick answer would be the system monitors and corrects the RPM and phase relationship between the left/right propellers to reduce noise and vibration.
Beyond that the system gets a little complicated. Having never worked on propeller aircraft other than a short stint working OV-10's in the Air force, it took me quite a while to understand the complicated workings and relationships that sophisticated Propeller aircraft employ. If you would like I can try to explain it here now. Having attended a 2-week Hartzell Propeller course in Ohio this is what I came away with.
The system I work on employs two modes or is called "dual control" as explained above. RPM tuning is designed to maintain both propellers at one of the two selected speeds. Cruise or Climb and these two speeds are programmed into the Syncrophaser Computer. When the Condition levers (RPM) contact a micro-switch, called capture range, for a set amount of time, in the case of the Do328 it is 7-8 seconds I believe, it compares the two values via a Hall effect sensor. This hall effect sensor is basically an engine RPM pickup sensor similarly used in automobiles. The syncrophaser can alter the RPM +or-3%.
Phase relationship is the other operating mode it basically monitors and compares the phase relationship between the two propellers. A microprocessor generated clock signal is used to determine the amount of phase error. A syncrophasing coil mounted on the Constant Speed Unit of the engine will change one propeller speed slightly to be in exact phase with the other prop. In a nut shell you wont get that humm humm humm sound, like on C-130's. This system is basically passenger comfort.
I hope this was helpful, it fully took me 7 months to finally understand propeller theory and operation, so if it doesn't sink in don't sweat it.