Zelda is not the one with the sword
It is the most common mix-up in gaming. ZELDA is the PRINCESS. The green-clad HERO you actually control is called LINK, and the series is named after the person he spends most of it trying to rescue.
The name itself was borrowed. Nintendo's designers took it from Zelda Fitzgerald, the American writer married to the novelist F. Scott Fitzgerald, simply because they liked the sound of it and thought it suited a princess in a story meant to feel like an old LEGEND.
A childhood spent looking into caves
Shigeru Miyamoto grew up in the countryside near Kyoto, wandering through fields and woods with no map. The story he tells is of finding the mouth of a cave one day, coming back later with a lantern, and edging inside to see how far it went.
That afternoon is the entire series. A Zelda game hands you a world with no arrows pointing anywhere, a cave you have not been in yet, and a strong suspicion that something is hidden behind the waterfall. The first one, in 1986, shipped on a gold cartridge with a battery inside — one of the earliest console games that let you save a QUEST and come back to it, because it was far too big to finish in one sitting.
A world that obeys its own rules
The 2017 game Breath of the Wild works because it runs on a few consistent rules rather than a script. Fire burns grass, and burning grass makes hot air that will lift a paraglider. Metal conducts electricity, so carrying a metal SWORD in a thunderstorm is a genuinely terrible idea — and a metal box can be dropped on a switch, or left out as a lightning rod for an enemy standing next to it.
The designers did not plan most of what players do with this. They set the rules and let people work out how to ride a SHIELD down a mountainside or start a forest fire to cook dinner. Puzzles end up with half a dozen answers, because the world has no idea which one you were supposed to use.
Courage, wisdom and power
The TRIFORCE splits three ways, and the split is the series' argument in miniature: COURAGE for LINK, WISDOM for ZELDA, POWER for GANON. The villain has strength and nothing else, and it is never quite enough.
Everything else returns game after game like a folk tale being retold — a MASTER SWORD waiting in a stone, a FAIRY who heals you, a DUNGEON with a locked TEMPLE at the end of it, a BOOMERANG that comes back, RUPEEs hidden in the grass. Each new game shuffles the same handful of pieces, which is exactly why fans argue so happily about what order any of it happens in.
One detail did change, briefly. LINK is left-handed in almost every game, but for the Wii version of Twilight Princess the whole of HYRULE was mirrored so that he swung his SWORD right-handed, because that suited the motion controls most players would be waving about.