Difference between a virtual function and a pure virtual function

A pure virtual function is usually not (but can be) implemented in a base class and must be implemented in a leaf subclass.

You denote that fact by appending the "= 0" to the declaration, like this:

class AbstractBase
{
    virtual void PureVirtualFunction() = 0;
}

Then you cannot declare and instantiate a subclass without it implementing the pure virtual function:

class Derived : public AbstractBase
{
    virtual void PureVirtualFunction() override { }
}

By adding the override keyword, the compiler will ensure that there is a base class virtual function with the same signature.

For a virtual function you need to provide implementation in the base class. However derived class can override this implementation with its own implementation. Normally , for pure virtual functions implementation is not provided. You can make a function pure virtual with =0 at the end of function declaration. Also, a class containing a pure virtual function is abstract i.e. you can not create a object of this class.

A virtual function makes its class a polymorphic base class. Derived classes can override virtual functions. Virtual functions called through base class pointers/references will be resolved at run-time. That is, the dynamic type of the object is used instead of its static type:

 Derived d;
 Base& rb = d;
 // if Base::f() is virtual and Derived overrides it, Derived::f() will be called
 rb.f();  

A pure virtual function is a virtual function whose declaration ends in =0:

class Base {
  // ...
  virtual void f() = 0;
  // ...

A pure virtual function implicitly makes the class it is defined for abstract (unlike in Java where you have a keyword to explicitly declare the class abstract). Abstract classes cannot be instantiated. Derived classes need to override/implement all inherited pure virtual functions. If they do not, they too will become abstract.

An interesting 'feature' of C++ is that a class can define a pure virtual function that has an implementation. (What that's good for is debatable.)

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Note that C++11 brought a new use for the delete and default keywords which looks similar to the syntax of pure virtual functions:

my_class(my_class const &) = delete;
my_class& operator=(const my_class&) = default;

See this question and this one for more info on this use of delete and default.