The first game is simple. Hearts in this series are pretty much just souls. The Heartless are creatures of pure darkness who instinctively and mindlessly seek out hearts and devour them. When the Heartless eats a person's heart, that heart is shrouded in darkness and becomes a new Heartless. That's bad enough, but every single world also has a heart. If the Heartless infect a world's heart, that world is snuffed out.
You play a kid named Sora who lives on an island with your friends Kairi and Riku. All three of you want to travel, but your boating trip is cut short when your world gets eaten by the darkness. You get a magic Keyblade (which you learn can be used to "lock" a world's heart away, keeping it safe). Kairi and Riku go missing. You meet Donald and Goofy who are looking for King Mickey. The three of you travel between worlds, killing heartless and sealing world hearts. You discover a bunch of Disney villains are seeking the Princesses of Heart, pure maidens that have no darkness in their heart. Six of these are traditional Disney princesses, the seventh is your friend Kairi. Gathering all seven of them opens the door to Kingdom Hearts, the heart of all things and a source of great power.
Long story short, Kairi's heart ended up locked away in Sora's heart. Riku is (somewhat willingly) possessed by a dude named Ansem who is actually a Heartless that maintained his human form and mind. Ansem/Riku wants to unlock Sora's heart, you beat him, but Sora unlocks his own heart to free Kairi. He turns into a little nobody Heartless, but Kairi turns him back. The three heroes go hunt down Ansem and end up at the door to Kingdom Hearts. After an ass-whooping, Ansem opens the door with the expectation that the darkness inside Kingdom Hearts will give him vast power, but it turns out that Kingdom Hearts is pure light which just fuckin' obliterates him. All's well and good, but the Heartless are about to go in the door and just eat the shit out of the heart of all things, so Sora has to close and lock the door.
Tough shit, he can't by himself. Luckily, Riku and King Mickey are on the other side of it. The three of you are able to seal the door shut, keeping Kingdom Hearts safe and restoring all the lost worlds.
And then Chain of Memories comes out and things get a little silly.
And then KH2 comes out and things get a little dumb.
And I'm not positive, but I think Birth By Sleep is when things get super dumb.
Or to sum up in a different way the hilariously convoluted nature of Kingdom Hearts: The enemies called Heartless have no body, they just have a heart. The enemies called Nobodies have no heart, they just have a body.
Then Dream Drop Distance got even dumber with "sleeping worlds that dream."
DDD added time travel to Kingdom Hearts. That's really all that needs to be said. ---