Special Services at BA basically provide additional services for premium passengers. I think of them as something akin to a concierge service related to BA Travel. E.g. I have arranged fast track immigration clearance at BKK via special services when flying in F and with little time to spare upon arrival.

I thought they tended to be backroom, rather than "front of house" staff and basically act as a point of reference for non standard requests, which the PAX raises with front line staff. I think they are reactive rather than proactive (for Golds) and clearly there is a limited amount they can do (you are not going to get moved from Y to F for instance ).