It's pretty spoilerish, so if you're the type that doesn't want to know how King Kong ends, you might want to steer clear.
The merry band of noble heroes has fallen for the evil emperor Gesthal's ruse (seriously? they fell for that? If that "oh, I was bad, but I'm good now" trick isn't the oldest one in the book, it's probably number two) and must now confront him on the creepy floating continent. That's standard enough fare for a Final Fantasy game. Truthfully, it'd be weirder if you didn't have to fight a crazed, magic-infused emperor on a floating continent at some point.
Gesthal's right hand man, Kefka, has served to this point as a murderous psychotic underling, but you never doubt that he's got a few tricks up his sleeve.
|Along with some seriously unresolved anger issues|
|Only that's not how it goes down|
Gestahl decides that his lapdog needs to be put down and prepares to kill him. Only Kefka's oddly unconcerned. Turns out he's been paying very close attention to how this whole thing works. He blasts the horrified emperor (and nudges him off into the abyss below, just because he's a bastard)*. The heroes are helpless to do anything but run while Kefka blasts the entire world into pieces. Even the airship gets torn in half (which sets up a potentially poignant scene with Celes and a certain clifftop)
It's been said that the game goes a ways downhill after this point, and that's probably an accurate assessment. This represents the high point of the game, and everything else is simply (re)building your party for the final showdown. It's hard to hold that against the game, though. After all, there's only (in my opinion) seven games with a higher high point.
*For a bit of extra awesomeness, check out the Game Boy Advance remake, and take a look at Kefka's eyes as he's shaking his finger at Gesthal's ineffectual attacks. Pretty awesome touch for what the graphics allowed.