What do these explanations for propellor RPM increases mean?
The troubleshooting section from the Hartzell Propeller Owner's Manual No.411 states:

B. Engine Speed Varies with Flight Attitude (or Airspeed)
   (1) Small variances in engine speed are normal and are no
       cause for concern.
   (2) Increase in engine speed while descending or increasing
       airspeed:
       (a) Non-feathering ( )(A,B)1 series propeller:
           1 Governor is not increasing oil volume in the
             propeller.
           2 Engine transfer bearing leaking excessively
           3 Excessive friction in the blade bearings or pitch
             changing mechanism


Reasons 1-3 relate to the propellers inability to adjust its blade angle to maintain a constant RPM when descending and airspeed is increased on non-feathering propellers.

The transfer bearing allows governor controlled oil into the crankshaft interior then to the propeller hub. If the bearing is leaking excessively the oil may be leaking back into the crankcase and there may not be enough oil pressure going into the hub to increase the propeller blade pitch and slow the engine down. 

If there is excessive friction in the blade bearings the propeller blades may not move freely within the hub even when adequate oil pressure is supplied by governor and oil system.