I'm Danish, I didn't really understand that for a long time. I would say that it doesn't mean Danes are super happy, it's just that the good economy, free education, free health care and strong social benefits makes it much harder to be very unhappy. So just happier on average.
Coming from Sweden I very much relate to this. For what it's worth I've also often wondered to what degree these types of polls control for a societal aversion against / lack of comfort with expressing displeasure and unhappiness.