Everyone has national health insurance, but you also get to choose where to go, and some doctors also offer non-insured services that you can pay for out of pocket.
The result is universal coverage combined with a competitive market that drives prices down and encourages innovation.
I know this is just anecdata, but having held an insurance card there for a while, our family was always able to see our family doctor the same day we called. And the one or two times a specialist or emergency room was needed, there was minimal hassle.
I'm sure there are problems with it, too -- I just don't know what they are. As a customer/patient, it seemed to work far better than the American system I'm used to.