VAGcat says it's part 15 in this diagram.
1J0906283C
electro change-over valve
The only function I know of for such a valve on a TDI engine is the control of the antishudder flap in the inlet, just upstream of the EGR.
On my engine (ASV) the vacuum changeover solenoid is mounted on the inlet manifold, close to the flap actuator. Perhaps on yours it's on the firewall along with the other vacuum solenoids? A picture would confirm.
Alternatively, can you tell us if it has an electrical connector and two pneumatic pipes (vacuum/air pressure)? If so, then it's almost certainly the antishudder valve controller.
Your question is very specifid "Could anyone enlighten me as to what this part does to see if it is the cause of my engine hesitation at light throttle and high idle tick over? " Why do you suspect this part? Has it been changed, damaged or disconnected recently?
The antishudder valve is normally open and only closes for a second or two when the engine is turned off. This is to reduce the volume of air sucked into the now-dead engine, which has to be compressed by the energy from the flywheel. Less air means less pressure and less shudder. I'm not sure how this could cause issues at idle or low revs.
Made in USA?
Where was the car made?