Zelda: Breath of the Wild's biggest success as a game is in its ability to instill feelings of wonderment in the player. The opening sequence being probably the clearest demonstration of this. When the game begins, Link is awakened by a voice from his 100-year slumber in a dark, blue, monochrome temple.
After receiving the Sheikah Slate and a poorly fitting pair of pants and a shirt Link climbs up a small ledge and out the temple entrance and into the bright world. Control is wrested from the player and he runs up to the top of a cliff and looks out onto the post-apocalyptic wilds of BotW's Hyrule and as you can see below, it is breathtaking. Without ever seeing the game map, BotW lets the player know that the environment is humungous and varied with the volcano, marshes, and Hyrule castle all visible within the first several minutes of the game. This variation of climate and scenery gives BotW its feel of being an epic quest as Link traverses the land discovering new and incredible locations. But, as important to this game as the environment is, so is the mechanics by which Link explores his world.
BotW is able to continually keep the player engaged with the mechanics of the game in new and creative ways. Within the first few hours of play, the player is granted the four special abilities, as well as a paraglider, Link will use throughout the entire game to both manipulate and traverse the world's unforgiving landscape. Even though you are granted these tools and are taught the general principal around using them, players will have to reason out how they can use these tools in different ways throughout the game. For instance, Stasis is a spell which allows Link to freeze objects (and later creatures) in time. The obvious application of this is to freeze moving platforms so that Link can safely cross them. What is not obvious is that Link can hit the frozen objects with his weapon in order to store kinetic energy inside of it until time starts again at which point the object goes flying.
Breath of the Wild encourages this type of inventiveness to a fault. At one point I was watching my friend play and she was solving a motion control puzzle wherein a ball would drop from the ceiling and you would have to tilt the controller in order to get that ball to go through a maze. After struggling with this for some time she flipped her controller upside down and the whole puzzle flipped to the other side which was smooth by doing so, she circumvented the puzzle entirely whereas I did the puzzle in the way which was intended.
This is the not-so-secret secret inside of Breath of the Wild. The player is encouraged to test the boundaries in order to figure out what they can or cannot do and rewards that inventiveness by allowing great freedom. The game doesn't arbitrarily pull the rug out from under the player or reinvent the rules the player has grown accustomed to. In most cases, clearly, there was a method the designers intended of going through the game but, once you knew the rules Hyrule abides by, you can cheese your way through much of the game.
This is what sets this game a cut above. Where other open world games differ from BotW is in their comfort with breaking the rules of the of the world in order for the game to progress. Usually, direct combat is encouraged. Breath of the Wild couldn't care less if you spend 30 minutes throwing bombs off a cliff to kill a Hinox without ever hitting it with an actual weapon, similarly, it doesn't care if you try to kill Calamity Ganon with 3 hearts and no armor. In many ways, it resembles a sandbox game with the attention to detail of an adventure game.
The freedom of this game and the dedication to the stated mechanics paired with the depth of attention given to building the world has clearly resonated with a wide player base and has helped this entry of the Zelda series find its spectacular success.