The original was a really weird game for the time being. It was top-down when most games were sidescrollers, for starters; it certainly wasn't the only bird's eye view game on the console, but it is generally agreed to have been the first widely successful title to use this otherwise new concept. This sounds like a stylistic choice, but it was huge at the time. Most of the successful games on the market were linear side-scrollers of some kind. Mario clones, Contra clones, Double Dragon clones were the name of the game. There were some weird ones, like sports games or board game ports, but those were either the exception or bargain-bin shovelware.
Zelda was different. Dropping jumping in favor of seeing Link from the sky was a huge trade-off. No longer did the player have to follow the preset path, beat up all the ninjas or goombas or aliens, and punch the final boss to death. You couldn't do that, even. The player was put into a massive game world; they had no map, no obvious direction to their goal. Your biggest hint was that if you bothered to read the manual, you knew Ganon was at Spectacle Rock on Death Mountain, and if you read the hilarious opening scroll, you knew you had to assemble the Triforce to kill him. Scant few NPCs told you where the secrets were. You had to find the dungeons on your own, figure out how to kill the bosses, collect the items you needed. The game developers later stated in interviews that they fully expected players to make world maps on graph paper, keep notes, share advice with friends.
The structure of Breath of the Wild isn't the only thing reflective of a return to this philosophy. The new mechanics--a jump button, climbing everything, a more open-ended equipment system--are a deliberate attempt to be the next bird's-eye view. Zelda 1 afforded players a huge world they could take on in any way they wanted--something that became lost to a degree as the later games came, with the Nintendo 64's necessary waist-high fences giving players then-unprecedented mobility but leading to Wind Waker, Twilight Princess, and Skyward Sword becoming more restrictive than their gaming contemporaries. Climbing everywhere and jumping everywhere afford the player new opportunities to explore the world in a way that the games since Ocarina of Time haven't offered.
Nintendo's been going after this for a while. Skyward Sword was built to challenge assumptions. Link Between Worlds deliberately evokes Link to the Past's design. And Breath of the Wild? Breath of the Wild is Nintendo finally being able to realize their goal--this isn't just a new Zelda. This is Zelda 1 the way it was meant to be played, free of the restrictions of the NES, free of the restrictions of the Nintendo 64. This is the Metal Gear Solid to Metal Gear 1, the Street Fighter II to Street Fighter I--the original vision done the way it was meant--just on a 30-year time scale.
...Did I just turn an intended 1-paragraph forum post into an essay about the evolution of a video game feature again? What the hell? This happens every time.