calculating factorial using template meta-programming

I do not understand how this piece of code (from Wikipedia) works:

template <int N>
struct Factorial 
{
    enum { value = N * Factorial<N - 1>::value };
};

template <>
struct Factorial<0> 
{
    enum { value = 1 };
};

// Factorial<4>::value == 24
// Factorial<0>::value == 1
void foo()
{
    int x = Factorial<4>::value; // == 24
    int y = Factorial<0>::value; // == 1
}

• What is this weird template that takes <int N>?
• What is this second weird template <>?
• What are the enumerations for?
• What is the advantage of using this rather than normal runtime factorial calculation?
• How often do you people use this? I have been using C++ for a while now, but never used this before. How big a part of C++ was I missing out on?

Thanks!