Having lived in several European countries I'd say Finland has probably one of the weaker health care systems.
* every legal resident has access to basic health care in their own municipality. A visit costs around 30 euros, max 700 euros a year (Which is a lot compared to Germany, cheap compared to the US). Queues can be long, several weeks. Negotiation skills help, but as a foreigner you might get blocked completely as a trouble maker if you think to negotiate in English
* nearly everybody with a full employment contract has basic health care coverage by their employer at a private provider. Normally you get an appointment the next day or so and you pay absolutely nothing. So most employed people just skip their "free" public health care, because it is worse. Yes, the employement health care is subsidized by tax money (although they are cutting back). This is not mandatory, so the details especially for mor expensive treatments and examinations vary a bit. When your employer stops paying you need to fall back to public service or pay yourself.
* for kids around 50% have private insurance to avoid the queing at the public service
* medicines are expensive compared to Germany, but cheap compared to market prices. Well, basically they are covered by the public health insurance, but the compensation is far from 100%, own contribution max 600 euros a year.
* hospital care is 50 euros a day, max 700 a year. There can be some queues, but for acute cases there should be no problem. (Non-acute cases can be a pain.)
In real serious cases the 1500 or so Euros you pay a year is of course cheap compared to complete bankruptcy or even remaining without good treatment. Being relatively healthy paying several 100 Euros a year is more than you would pay in many European countries with a public health insurance systems.