Now I don't get what is a Primary insurance exactly- is it the Universal Health Care System ?
No. "Primary" and "secondary" generally refer to the order in which the insurance will be triggered upon someone filing a claim. If someone has both primary and secondary insurance, and the primary insurance fully pays for the claim, then the secondary insurance is not triggered. In other words, secondary insurance may cover what the primary insurance fails to cover. In the US, our healthcare insurance is primary insurance. If I suffer some misfortune that is fully covered by my healthcare insurance, then it doesn't matter whether I also have secondary insurance. However, if I suffer some misfortune that is not covered (or is only partly covered) by my healthcare insurance, then the secondary insurance may cover it (or cover the portion not paid by my primary insurance).