A lot of it comes from turning previous obstacles into new opportunities. Walls and mountains are no longer barriers, they're opportunities for player freedom -- you can climb or glide to your heart's content. Nintendo also embraced a "multiplicative" approach to gameplay where physics and chemistry allow for intuitive (and seemingly endless) solutions, such as fanning a bomb to propel it or cutting down a tree to cross a gap. And instead of relying on canned puzzles with only one right answer, the game hands you situations and goals that leave the approach up to you.
Even the decision to support the Switch added some freedom, Nintendo says, by letting you play how and where you like.
It's a lengthy discussion, but worth watching if you're interested in what makes Breath of the Wild tick. The talk is also insightful if you're interested in some of the behind-the-scenes aspects of the game's creation. It reveals that the game originally existed as a pseudo-2D prototype (to test its underlying concepts), that the team initially brainstormed wild ideas for their next Zelda game, and that the cell-drawn yet detailed look is a purposeful balance between playability and helpful realism. Even if you have no intention of playing the game, this might just give you newfound appreciation for the effort that goes into a blockbuster release like this.