Your confusion stems from a crucial difference between Java and C++.
In Java if you write
MyClass var = whatever;
your variable var is a reference to the object returned by whatever. However, in C++ this syntax means "create a new object of type MyClass by passing the result of the expression whatever to an appropriate constructor, and copy the resulting object into the variable var.
In particular, your code creates a new object of type A, named c, and passes a temporary default-constructed object of type B to its copy constructor (because that's the only constructor that fits). Since the newly created object is of type A, not of type B, obviously A's method foo is called.
If you want to have a reference to an object, you have to explicitly request that in C++, by adding & to the type. However a reference to non-constant objects cannot be bound to temporaries. therefore you need to explicitly declare also the object you bind to (or alternatively, use a reference to a const object, and fix your foo member functions to be const, since they don't change the object anyway). So the simplest version of your code doing what you want would read:
// your original definitions of A and B assumed here
B b; // The object of type B
A& c = b; // c is now a *reference* to b
int main() { c.foo(); } // calls B::foo() thanks to polymorphism
However the better version would be const-correct, and then could use your original construction:
#include <iostream>
class A
{
public:
virtual void foo() const // note the additional const here!
{ std::cout << "foo" << std::endl; }
};
class B : public A
{
public:
void foo() const // and also const here
{ std::cout << "overridden foo" << std::endl; }
};
A const& c = B(); // Since we bind to a const reference,
// the lifetime of the temporary is extended to the
// lifetime of the reference
int main() { c.foo(); } //prints overridden foo
(note that I removed using namespace std; because it's a bad thing to do (and your code used explicit std:: anyway, so it's just redundant).
Note however, that C++ references are still different from Java references in that they cannot be reassigned; any assignment goes to the underlying object instead. For example:
#include <iostream>
class A { public: virtual void foo() const { std::cout << "I'm an A\n"; } };
class B: public A { public: void foo() const { std::cout << "I'm a B\n"; } };
class C: public A { public: void foo() const { std::cout << "I'm a C\n"; } };
B b;
C c;
int main()
{
A& ref = b; // bind reference ref to object b
ref.foo(); // outputs "I'm a B"
ref = c; // does *not* re-bind the reference to c, but calls A::operator= (which in this case is a no-op)
ref.foo(); // again outputs "I'm a B"
}
If you want to change the object you refer to, you'll have to use pointers:
// definitions of A, B and C as above
int main()
{
A* prt = &b; // pointer ptr points to b
prt->foo(); // outputs "I'm a B"
prt = &c; // reassign ptr to point to c
prt->foo(); // outputs "I'm a C"
}