You could ask that with a comment on the article, as most people here didn't read it and probably doesn't understand the scene->object relationship (as I didn't).
But answering to your first question, the one I can answer, a Singleton is a design pattern that forbids the instantiation of more than one object of a given "singleton class". In other words, if you have a Display class in your game, and want to make sure only one Display object is created at a time, you can make your Display class a singleton. So you'll avoid problems like creating two different game windows, in this example.
This is one way to do this:
public class Display {
public:
static Display getInstance() { //This is what you use on your game.
return SingleInstance;
}
private:
private Display(); //This is your constructor, private
//It is private so no one can create new objects
// but the first one.
static final Display SingleInstance = new Display(); // The only Display instance.
}