When you write extern int a; - it is a declaration not a definition. The extern keyword says that the variable is defined outside the function block.

The following code will explain this:

void func( );

void main ( )
{
    func ( );
}

void func ( )
{
    extern int var; //declaring a variable var which is outside the scope of this function (i.e. our global variable)
    printf ("%d", var);
}

int var = 10; //Defining a global variable. This can be in another file also

Note that we have declared (and defined) our global variable 'var' outside the func( ) block, and also way below the func ( ).
Had we defined the global variable 'var' above the func() block, we wouldn't have to declare it using the extern keyword.