What is a pure virtual function?

A pure virtual function is a function that must be overridden in a derived class and need not be defined. A virtual function is declared to be "pure" using the curious "=0" syntax. For example:

class Base 
{
 public:
  void f1();  // not virtual
  virtual void f2(); // virtual, not pure
  virtual void f3() = 0; // pure virtual
};

Base b; // error: pure virtual f3 not overridden

Here, Base is an abstract class (because it has a pure virtual function), so no objects of class Base can be directly created: Base is (explicitly) meant to be a base class. For example:

class Derived : public Base 
{
  // no f1: fine
  // no f2: fine, we inherit Base::f2
  void f3();
};

 Derived d; // ok: Derived::f3 overrides Base::f3

Abstract classes are immensely useful for defining interfaces. In fact, a class with only pure virtual functions is often called an interface.You can define a pure virtual function:
Base::f3() { /* ... */ }
This is very occasionally useful (to provide some simple common implementation detail for derived classes), but Base::f3() must still be overridden in some derived class.If you don't override a pure virtual function in a derived class, that derived class becomes abstract:

class D2 : public Base 
{
  // no f1: fine
  // no f2: fine, we inherit Base::f2
  // no f3: fine, but D2 is therefore still abstract
};

D2 d; // error: pure virtual Base::f3 not overridden&