"Allemansrätten" is the law you want to look up.

It's not that you can't keep people off your land if you really set out to accomplish that, rather, if you own a portion of uncultivated wilderness or forest, people can pass through, set up camp for a bit, harvest some wild plants they might find, etc.

If you don't set up a farm, a home, or start developing the land in some way that isn't just letting a forest grow to sell for lumber someday, then yeah, people get to be on your land. And if you own a giant piece of land, people only have to stay away from buildings and such. If most of it is just wilderness, those parts are fair game.

And there are some strict rules for what is and isn't allowed. Like you said, being a nuisance is not ok, and one of the biggest deals is that you can't damage trees. Trees are lumber, they are literally money growing on trees, so killing or damaging young trees can lead to extremely serious criminal charges.

You can use wood you find to set up a campfire, but you absolutely cannot hack parts off any living trees to do so. Dead branches that've fallen to the forest floor, only.

What this law means, is that anyone can just go outside the cities and other developed areas of the country, and go hiking out in nature. Or boating out in the archipelagos. You're allowed to explore and adventure, without having to dodge invisible lines on the ground defined by property rights. Instead, you only have to follow some basic common-sense rules, such as staying away from private buildings, not polluting or making noise, etc.