The correct answer is C) provide remote control for speed adjustment. The synchronizing motor on the generator governor is responsible for remotely controlling the speed adjustment of the generator. This allows the generator's speed to be adjusted from a remote location, which is important for synchronizing the generator with the power grid. The synchronizing motor does not directly drive the terminal shaft (A), turn the governor drive shaft during start-up (B), or power the generator synchronizing lamps (D). These other options are incorrect as they do not accurately describe the primary function of the synchronizing motor in the generator governor system.