It's nothing to do with files, and has to do with the classes/objects.
In that example, if you create a calculator object:
You could do
$calculator = new calculator();
$calculator->add();
If it's private, you could only call add() from within the object, so it would be like you'd create another method which WAS public, and when you called that, that method did $this->add();
Protected means if you extend the class by having another class like
Class myCalc extends calculator{}
That class could do $this->add() but you still can't do $calculator->add();
If you still don't get it, try using their example, and running some code with it, and changing private/protected/public to see what you can do with them.