At WDW it means a room in a special building or a special part of a building that you get special stuff - a lounge with food (light breakfast, snacks, drinks - alcoholic and non), a special place to check in, and a staff to make dining reservations and stuff like that for you.
Most hotels I've stayed at in the US have a concierge desk for all guests, but I think this is more what guest services is for at WDW.