I think it's a combination of everything that's been said before.
To a lay person, a game like FF6 is nigh impossible to get into. There are so many things to keep track of - different characters, different equipment which can only be worn by some, dozens of items to do different things, enemies and bosses which sometimes require special ingenuity to beat, nooks and crannies and secrets of all sorts that the power gamer can discover, etc. It's a lot to balance.
Chrono Trigger, I'd argue, thrives on its comparative simplicity. The storyline pulls few punches and is modeled in the style of a traditional epic, so it's easy to get behind. Characters don't have customization and they almost all can wear the same outfits. They're also each very strong and well-defined, and given a lot of screen time (which is not guaranteed in FF6). This is even true for villains (who doesn't love Ozzie, Slash, Flea, or Dalton?). Even small design choices like not entering a separate battle screen make it very easy for first time gamers to get what's going on. And, of course, it's time travel, a really simple idea. No concepts like summon monsters or nega worlds to understand. And, of course, the graphics and music are gorgeous. So when taken all together, Chrono Trigger is just a great game that's easy, quick, simple, and loads of fun all at the same time.
Incidentally, I'm sure this is why Chrono Cross didn't do nearly as well. While hailed as a great game by many, I think most people would have been content with a "Chrono Trigger 2," without too many elements changed. Instead, they got almost the exact opposite, with a storyline and battle system more complex than almost any other I've seen. It was great for hardcore fans to really delve into things, but it no longer had the approachable, anyone-can-play mentality that made the first such a runaway hit.