You use this second ה if you want to describe the specipic girl. For example: הילדה הרעבה (the hungry girl). Without it, it would be 'the girl is hungry' (הילדה רעבה). But here we say something about how she feels: she (the girl) is (feeling) hungry or not hungry. She feels sad (הילדה עצובה)..
I don't know if it was clear enough.. but I tried :)