It has 5 structures that are most similar to “dungeons”, and serve similar purposes of making you slightly more powerful and providing you with a mcguffin. They’re also part of learning about what exactly happened 100 years ago.
There’s no required order to do the dungeons in, but the game does try to guide you toward them in various ways. I think I did the first couple of them “in order” and then diverged. And, of course, as speed runs have shown us, you’re free to disregard them entirely and run straight to Ganon. But uh, save that for a second playthrough maybe, because they real meat of this game is in taking your time to carefully explore the world, which is very well-crafted.
You can save anywhere, and the game is also very generous with its autosave checkpoints.
Also, the 120 Shrines dotted across the map are quite satisfying mini-dungeons. Each one of them is typically equivalent to one of the larger “puzzle rooms” of a traditional Zelda Dungeon, but with often more of a reliance on the game’s surprisingly stable physics system. There are spatial navigation puzzles, environmental manipulation, logic challenges, and occasional straight-up fights. Some of the shrines are hidden behind riddles in the overworld, which will appear in your quest log after you read about them or hear about them from an NPC, and they feel a lot like finding secret stairs under a burnt tree or whatever in Zelda 1. You figure out what part of the landscape you’re supposed to shoot an arrow through or set on fire or whatever, and then a glowing shrine rises out of the ground. It’s neat. The shrines also comprise the game’s fast-travel system and you can freely teleport between shrines you’ve activated, starting from very early in the game.