When you have coverage under the Finnish social security system, you can apply and receive a personal health insurance card, the Kela card. This is proof of your eligibility to social security. When you are buying prescription medications at your pharmacy or paying for a doctor’s appointment at a private clinic, for instance, the Kela card entitles you to a discount.
All permanent residents in Finland are issued a Kela card. When you move to Finland, register at a local Kela office and complete the required application forms. You can read more about applying for the card here: KELA-card