This was a very big change for Zelda. Instead of the structure of doing dungeons (mostly) in order, Breath of the Wild delivers a vast open world and once you finish the tutorial, you can go anywhere you want to. You can even go straight to Ganon. You’ll probably die, but players much better than me have completed the game in this manner.
BotW gives you a lot of tools to work with, mainly the glider and runes. You have access to unlimited bombs, but the main instruments are Magnesis, which lets you move metal objects around (to make platforms, hurl at enemies or solve electric puzzles), Stasis which pauses an object in time and any force you put onto it (by hitting it) will be released in on burst, sending it flying, and Cryonis, which lets you create ice pillars in water.
Using all of these together in different ways takes experimentation, alongside discovering other ways to interact with the environment (burning grass creates an updraft you can use for gliding, for example). Some people (again, who are much better than me) can do crazy things with this.
This also makes a lot of the shines – miniature dungeons, most with puzzles – feel a lot more fun. Sure, you could try to finish puzzles in the “proper” way. Or you can cheat them. On one puzzle I was supposed to use ice blocks to guide a ball onto a switch, but I instead used Stasis and a well placed bomb arrow to sent it flying spectacularly to the switch. This never feels like you’re breaking the game, but rather just feels like you’re discovering different ways to reach your goal. Being able to do stuff in your own way without a game going “no, try again” feels quite fresh.
BotW does have some odd limitations. Weapons break after usage and your horse has to be nearby to be able to call it, however I feel like both of these encourage players to experiment with the other stuff – finding new ways to fight and navigate the beautiful world.
Breath of the Wild isn’t just an open world game – it’s a playground filled with amazing toys.