A game before its time, in more ways than one!
After the controversial love-it-or-hate-it side-scrolling RPG of Zelda II on the NES, A Link to the Past was a true return to form. Once again Link was dropped into the top-down, open world of Hyrule for a dungeon-seeking quest of epic proportions, but this entry expanded on the original Legend of Zelda in so many ways, introducing the lore and rules that would carry on to just about every game yet to come.
This game first introduced the concept of an ongoing timeline, and the notion that Link as a hero is not the same individual in every game, but rather a boy chosen by destiny to fulfill a prophecy of legend.
In the original game, the concept of the Triforce was explained as two sacred triangles representing Power and Wisdom, belonging to the evil pig-demon Ganon and Princess Zelda respectively. When the two are brought together, the one to possess both of them will rule Hyrule. Needless to say, the kingdom was under attack by Ganon, who wanted Zelda's Triforce of Wisdom so he could take the throne for himself.
A Link to the Past was set some time before then. As the story unfolds, a great war was fought in the past to gain entry into the fabled Golden Land where the Triforce resided, for it says anyone who touched it would have their wish granted. Eventually, the evil king of thieves Ganondorf found his way in there and claimed the Triforce, wishing to rule the land. Because his heart was not pure and he valued power more than anything else, the Triforce split into three pieces. As previously known, Power and Wisdom went to Ganondorf and Zelda, and a third piece, the Triforce of Courage, was bestowed upon Link, connecting the three characters by destiny.
The evilness of Ganondorf's wish also corrupted the Golden Land, turning it into the twisted mirror image of Hyrule known as the Dark World, and, reflecting his greed, turned Ganondorf into his groteque pig form, Ganon. Seven wise men sealed Ganon away in his own evil dimension at this point, preventing him from getting out and spreading his evil over the land. Interestingly, the next game in the series was Ocarina of Time, and most of the plot covered these events in Link to the Past's back-story, making OoT a prequel of a prequel.

With the setting established, in Link to the Past, Ganon has found a way to possess an evil priest named Agahnim from within the Dark World. Using Agahnim as his pawn, he ensnares the descendants of the original sages who sealed him, pulling them into his evil realm in attempt to break his dimensional confinement and take over Hyrule. During the commotion, Princess Zelda manages to send out a telepathic plea for help to the descendant of the hero who possessed the Triforce of Courage. The message reaches both a young boy named Link and his uncle, a knight in the Hylian army. After his uncle is sadly slain by monsters, Link takes up his family sword and shield and quests to save the day.
A Link to the Past incorporated everything that made the original game great, but expanded and improved upon it in every way. Dungeons now had multiple floors and levels, allowing for new puzzle elements such as items dropping to the floor below and walls too high to reach. The Hyrule overworld was lush with greenery, which could be slashed to find hidden rupees and heart pickups. Finally, there was a world map plotting out the game's major locations and giving Link an idea of the general direction he was meant to be heading in. Several new items were introduced, such as the Pegasus Boots allowing Link to dash across the screen and ram into enemies and obstacles. The Hookshot allowed Link to latch onto faraway items and pull them to him, or pull himself over bottomless pits like a grappling hook. The Power Glove gave Link the ability to lift heavy stones blocking his path. Link was now able to carry collectible bottles, in which he could hold fairies to restore his health when he fell in battle. He could also catch rarely-appearing bees and unleash them to attack unsuspecting enemies.
This was also the first time Link was given a green magic meter to accompany his health hearts, and several of his items would consume magic at different rates, requiring him to pick up little green flasks that would refill the gauge. The range of different areas, such as the Lost Woods, had multiple levels of layer and animation artistry, as leafy shadows and light filtered through the trees above. Dark caves could be illuminated by lighting torches with your lantern; more torches would mean more visibility. There were eye-poppingly impressive transparency effects, like flowing fog and a downpour of rain, complete with lightning flashes that would brighten the whole screen for a split second.

Many beloved series staples made their debut here. Link to the Past first gave us Hyrule's centralized population residence – Kakariko Village. It was a peaceful little town with a unique residence of NPCs, and happy chickens hopped about the local farm yard until Link felt mischievous enough to attack them. And yes, like all future iterations of the series, any chicken that was repeatedly attacked would eventually snap and summon an endless barrage of its bretheren to fly about attacking Link until he died or fled the area. The towering Death Mountain loomed over the entire of the map, with falling boulders and precarious rope bridges. The aforementioned Lost Woods was as confusing to navigate as in Ocarina of Time and Twilight Princess, and they even feature the pedestal remnant from the Temple of Time, the sleeping place of the legendary Master Sword.
The soundtrack not only reiterated the classic Hyrule Field theme music that has since become synonymous with the series itself, but also introduced several other series mainstays such as Zelda's Lullaby, Ganondorf's Theme, and the peaceful, sweeping Kakariko melody. It was a treat for the ears.
It's amazing how much the series has evolved over the years since this groundbreaking gem, and yet when the series turned 3D in Ocarina of Time, it's equally surprising to see how much the main formula stayed the same. The fact that the series transitioned into the third dimension so flawlessly while still feeling like a Zelda game is a true testament to how much of a mastery this game was. This game was even so influential that a group of 2D purists even once attempted to entirely recreate Ocarina of Time using the SNES graphics, but that's another story.