In C++ the “^” symbol is the bitwise exclusive or (xor) operator. For a single bit you have 0 ^ 0 = 1 ^ 1 = 0 and 0 ^ 1 = 1 ^ 0 = 1.
However, in the question you are refering to it is part of Microsoft special syntax for C++ development on the .NET platform known as C++/CLI or It Just Works.
Memory on .NET is garbage collected and references to objects will have to be tracked. This makes it impossible to reference these objects using a normal C++ pointer. Microsoft has decided to reuse the “^” symbol to declare a variable somewhat similar to a pointer that can reference an object on the managed heap.
^ (Handle to Object on Managed Heap)