I'm not sure what the technical term for it is but it's used for PHP's OOP (object-oriented programming). $vbulletin is a class and to access that classes members (variables of the class) or functions you can use the -> operator. So that just means that GPC['moderatorid'] is a member of the $vbulletin class. Quite a few programming languages use the same operator for this purpose.
Cool. I can understand that. Is there a reference manual anywhere that would have all of the vBulletin classes and functions as I can see the "->" operator used all over the place in the code. I've got a good grounding in programming and want to learn PHP so I thought I'd buy vBulletin as investment in my education. If I can understand what the code is doing, then I can make changes to it...