Lots of RPGs use an equipment durability system, but most of the time, durability never quite feels right. You're in the middle of a quest, and you've brought your favorite sword. Eventually, your sword starts to dull. You either burn through a repair tool, check in with a smith in town to get it fixed, or switch to one of the other weapons you're carrying and press on. It doesn't make the game any more difficult or deep, but it's built into the gameplay loop anyway, seemingly just for the sake of it.
Zelda: Breath of the Wild also features an item durability system, but it does so in a much more thoughtful, purposeful way—such that durability is actually an integral part of the overall game balance, and it makes Breath of the Wild a better open-world game.
In Breath of the Wild, every weapon has an assigned durability rating, appropriate to each piece of gear. Dinky wooden gear like the sticks you can pluck from trees or the clubs you snag from enemies have relatively low durability, as do rusty swords and other items like woodcutter's axes that you can use like weapons even though they're not really meant for fighting. More robust weapons like steel swords, broadswords, and battle axes have higher durability.
Once an item depletes its durability, it breaks and you can't use it anymore, forcing you to switch to another weapon in your inventory. This goes for melee weapons like swords and spears and magical fire rods as well as shields and bows.
Compare that a game like Dark Souls, one of the more well-known (and more Zelda-like) games to feature durability. Use a weapon, and it'll lose some of its luster. Bring it to its breaking point and it'll be way less effective until you repair it.
On its face, this seems pretty simple and not too terribly different than what Breath of the Wild is doing. But there's a key distinction: most of the weapons you'll find and use in Dark Souls have enough durability to get you from bonfire to bonfire (in Dark Souls, bonfires are a kind of checkpoint system), and an item available really early on in the game lets you repair your weapons at any bonfire for a trivial fee (in the sequels, item repair comes free of charge from the beginning of the game).
In Dark Souls, durability might as well not exist, given that you basically have to be deliberately avoiding bonfires to break most pieces of gear. It's just a minor inconvenience if you somehow manage to neglect your equipment.
But in Breath of the Wild, equipment is meant to be disposable. Most of the items you'll find in the game's opening area, the Great Plateau, break after somewhere between 10 and 20 uses. You're supposed to be constantly foraging for and swapping out gear, not just fixing it endlessly at bonfires, because you can count on the fact that everything you discover will break at some point.
That means when you find a powerful weapon, it's not necessarily going to let you steamroll every enemy in sight. You might want to save it for those moments when you really need it, because if you use it to hack through low-level grunts, you'll probably be wasting its durability and therefore its attack potential.
Constantly forcing the player to make decisions about when to use their best gear has a balancing effect on the entire game. It means that the game difficulty is highly sensitive not only to the weapons you've found and decide to use at any given point, but also to the way you budget those weapons' durability.
That added balance gives players more options for modifying the difficulty to suit their playstyles.
Do you decide to use the most powerful weapon available to you at any given time, knowing that it'll break sooner but also that you'll have an easier time with the enemies in the area you're already exploring?
Do you try to maximize the gear you're carrying to mitigate the possibility that you'll be left in a tight spot if all your weapons break?
Or do you ignore the advice of the classic old man and try to go it alone without a sword at your back, making do with the highly breakable sticks and clubs you find at enemy camps?
Whatever you choose, your approach to managing your inventory is sure to be markedly distinct.
Most Zelda games don't ask players to make these kinds of on-the-fly strategic decisions about which items to use. You'll generally find the weapons that are required to beat the game, and can collect (or avoid) Heart Containers, potions, and ammo upgrades if you want to modify the difficulty. Likewise, in Dark Souls games, you can choose to minimize or maximize your stats or farm certain consumables to determine how tough your quest will be, but item durability is rarely, if ever, a factor.
If you're going to survive in the wilds of Hyrule, however, you're going to need to be resourceful. In Breath of the Wild, the gear you decide to use in any situation always impacts the gear that's available to you later. There's even a risk vs. reward element to taking on enemies. They could be guarding better gear, or you might just burn through your equipment for a piece of ore. That positions item durability as a key strategic element and makes it critically important to explore each area and exploit whatever gear you can find.
For an open-world game, this is huge, because it means every enemy encounter depletes your resources, and any environment or point of interest could be home to a piece of gear that you need to become more powerful or keep your inventory in top shape. I can't think of a better gameplay incentive to discover every nook and cranny of Breath of the Wild's gigantic world and see what treasures await me.