It's just general obligatory health insurance you get when you are employed or registered as unemployed. Each month some part of salary is deducted to it. In general there is wide variety of treatments and screenigs, however queues are sometimes so long it's even pointless to wait because you either heal by yourself or die in a meantime :D
For example after deel cut on my finger I had appointment in two months for stiches removal, except you have to remove these much sooner. I did this myself. My friend after fall from a skateboard has his rehabilitatiom appointment in more than 3months, which once again is absolutely pointless.
I'm still really happy with such system when I read about American health care.
How does it work in Romania?
I think it works just about the same as in Poland but I never heard about stiches removal in 2 months time, if it did happen, one way to go about it would be (instead of removing them yourself) to go to the emergency department and someone will help you there for sure.
Myself, I don't have or had any kind of insurance but was able to get treatment in the hospital for more than 3 days which are for free anyway even without insurance. What's over 3 days, you need a doctor to vouch/sign for you that your life could be in danger if they are to get you out of the hospital.