Prior to 1994, there wasn't much of an RPG market in the United States. Companies didn't feel like they had enough cause to translate games from a genre that just wasn't catching on very well. Square was far from its immense status in the Playstation years, its strongest title so far being Final Fantasy II (a.k.a. IV). And that didn't have all that much mainstream success, if Square's decision not to translate Final Fantasy V was any indication. Enix had made a half-hearted bid with Soul Blazer a couple of years back, and would emerge with the spectacular Illusion of Gaia in late 1994, but that would be too late - that was when the utterly brilliant Final Fantasy VI came out under the number III stateside.
Final Fantasy VI concentrated far more on such things as "plot" and "characters" than its predecessors (especially Final Fantasy V, which had been practically devoid of both). The result was an enormous epic, with a cast of fourteen playable characters. The beauty of the game is that despite having so many characters, none of them are alike. First, technological advancements had made possible far more detailed sprites than the heavily pixelized little squares of Final Fantasy IV. Second, each character had a very unique face thanks to Amano's stylized portraits, and a unique character theme in addition to that. And third (and most important), no character was left out of the plot, and every attempt was made to flesh them out as much as possible beyond their initial dialogues/motives when joining the party.
Final Fantasy VI was also different from its predecessors in mood, which is often morose and gloomy. (While there's some very half-assed comic relief, it comes rarely, mostly in the form of ridiculous bad guys like the octopus Ultros.) The idea of "heroes fighting The Evil Empire" is pretty basic, but when all of those heroes are so well developed, with long stories of how the Empire came to greatly hurt them, the result is a story that really pulls you in. Each character has been in some way betrayed or manipulated; the most memorable example is the knight Cyan, whose family's death is perhaps one of the most tragic moments in RPG history. And while the villain Kefka's clownish appearance and grotesquely unforgettable laugh may be funny and comical, after he commits genocide it becomes rather disturbing. And just when you really, truly think you've reached the final dungeon and the story is about to end, Kefka actually emerges victorious and blows the world up. The remaining half of the game puts you on a solitary island with one character, and you're to find everyone else. The post-apocalyptic World of Ruin is relentlessly bleak, from the sight of its world map (and the dirge that is the overworld theme) to the dialogue of the villagers to everyone's general hopeless attitude. (Your starting character attempts suicide after she's left alone on the island, for instance.) Ruin and emptiness pervade the brave new world - some towns are devoid of life, some towns are completely obliterated, and the grass itself turns a sickly yellow (and, of course, the enemies are a sight uglier than before). The most memorable example, however, is the strange Ancient Ruins you might stumble across while travelling, which add their own tragic story to the pile.
Despite Nintendo's censorious "family-friendly" crap, still in full effect in 1994, the bleakness is still quite clear, and even if the people aren't allowed to say "death" it's blatantly obvious that the concept is more than present. For this, Ted Woolsey's translation is to be highly commended. Advances in technology also gave Nobuo Uematsu the means to make a truly epic soundtrack. Final Fantasy VI's soundtrack is in fact so good, it's one of the few I'd recommend buying separately on CD. The graphics represent the best of the times, certainly the best of 1994 (up yours, Donkey Kong Country). You will not forget some of the sights you will see (Vector in flames, the World of Ruin overworld map, etc.). Absolutely every part of this game works on every level.
From here on, the path to the top was clear, and was paved with more landmark titles like Chrono Trigger, Final Fantasy VII, and Xenogears. While all of those came to eclipse Final Fantasy VI, one could argue that their success was only due to further developing the things that worked so well in it. Square had been aiming for greatness since 1989, since they took on Enix at their own game with Final Fantasy I, but this was the first time they truly achieved it.