What are "::operator new" and "::operator delete"?

:: tells the compiler to call the operators defined in global namespace.
It is the fully qualified name for the global new and delete operators.

Note that one can replace the global new and delete operators as well as overload class-specific new and delete operators. So there can be two versions of new and delete operators in an program. The fully qualified name with the scope resolution operator tells the compiler you are referring to the global version of the operators and not the class-specific ones.

the new keyword (used alone) is not the same as the operator new function.

Calling

Object* p = new Object(value);

is equvalent in calling

void* v = operator new(sizeof(Object));
p = reinterpret_cast<Object*>(v);
p->Object::Object(value); //this is not legal C++, it just represent the implementation effect

The operator new (or better the void* operator new(size_t) variant) just allocate memory, but does not do any object construction.

The new keyword calls the operator new function, but then calls the object constructor.

To separate allocation from contruction, a variant of operator new is declared as

void* operator new(size_t, void* at)
{ return at; }

and the previous code is typically written as

Object* p = reinterpret_cast<Object*>(operator new(sizeof(Object))); //no contruction here
new(p) Object(value); //calls operator new(size_t, void*) via keyword

The operator new(size_t, void*) does nothing in itself, but, being invoked by the keyword will result in the contructor being called.

Reversely, destruction and deallocation can be separated with

p->~Object();
operator delete(p); //no destructor called

instead of delete p; that calls the destructor and then operator delete(void*).