[ From the blog ] 

Polymorphism allows for different function implementations to be called, depending on values only known at run time. For instance:

class BaseA {

 public:

 virtual void foo(){cout<<"Base";};

};

class A: public BaseA {

 public:

 void foo() {cout<<"Child";};

};

A a;

BaseA & base = a;

base.foo(); 

Will print "Child".

"Pair polymorphism" is when you want a specific function implementation to be called based on the run time value of two different instances of a class. For instance in the case of:

class BaseA {};

class BaseB {

 public:

 virtual void foo (BaseA & a) = 0;

};

class A: public BaseA {};

class B: public BaseB {

 public: void foo (A & a);

}; 

You would want that somehow "void B::foo (A & a)" will be called. The code I posted does not do this.
There is a way to do this, but it requires for a class to know about the implementation classes. It is not a problem in some cases. However, sometimes you want to have an abstraction layer.
An abstraction layer is a set of classes or interfaces, that have no methods or "don't know" anything about the classes that implement them. For instance you can have a graphics abstraction layer.
You could implement this layer with DirectX. However, this layer will make it easier to afterwards add an implementation with OpenGL without having to make a lot of changes, even if the game is already completed.

How are we going to have a "pair polymorphism" in this case? One solution is using dynamic casting. You can cast a pointer of a parent class to it's child class(in case the run time value really points to an instance of that class).
Some code:

class BaseA {};

class BaseB {

 public:

 virtual void foo (BaseA & a) = 0;

};

class A: public BaseA {};

class B: public BaseB {

 public:

 void foo (BaseA & a) {

 foo2 (dynamic_cast(a));

 }

 void foo2 (A & a);

}; 

I was asked by someone how this can be done without dynamic casting, because he doesn't like dynamic casting. I found a way, but it ain't pretty, and I honestly can't find any advantage of using this code instead of just using dynamic casting. But here it is:

class BaseA {

 public:

 virtual void DynamicCast() = 0;

};

class BaseB {

 public:

 virtual void foo (BaseA & base) = 0;

};

class A;

class Caster {

 public:

 A * a;

};

class A: public BaseA {

 public:

 Caster * c;

 void DynamicCast() { c->a = this; }

};

class B: public BaseB {

 public:

 Caster * c;

 void foo (BaseA & base) {

 base.DynamicCast();

 foo2 (c->a);

 }

 void foo2 (A & a);

};