The original object of the class A will be changed.
When you are using a const member function then the function deals with const T *this
where T is the class type.
That is data members of the object are considered constant.
For a referenced type it could look like
A & const a;
However references themselves can not be constant.
That is for example this declaration
int x;
int & const rx = x;
is invalid and does not mean the same as
const int & rx = x;
So the class B has a reference that points to a non-constant object and using the reference the object can be changed.
Compare with the following declaration of the class B
class B
{
public:
B(A * a) : a(a) {}
void constStuff() const { a.doSomeStuff(); }
private:
A *a;
};
Then then a constant member function is used the data member is considered like
A * const a;
(pointers themselves may be constant) that is the pointer itself that is constant not the object pointed to by the pointer and you can not change the pointer itself but you can change the object pointed to by the pointer.