This is what the Airbus 34-6 book says:
The trim tank transfer system controls the aircraft's Center of Gravity (CG).
The system either transfers fuel to the trim tank (aft transfer), or from the trim tank (forward transfer).
This movement of fuel changes the aircraft's CG.
When the aircraft is in cruise, the system optimizes the CG position to increase fuel economy by reducing drag.
Normal operation is automatic, but the crew can manually select a forward fuel transfer.
The Fuel Control and Monitoring Computer (FCMC) calculates the aircraft's CG and compares it to a target value. (This target depends on the aircraft's actual weight. See AFT CG Target Graph below).
Based on this calculation, the FCMC determines the quantity of fuel to be moved aft or forward in flight.
It does it very effectively.