In general those games worked by splitting data between the discs based on where in the game story its needed. A lot of data will be duplicated on each disc, if it's something that is needed wherever you are in the game. For example the models/textures for characters. It's generally things like video and audio for story dialogue that are split between the discs because they are only needed at a specific point in the game. I know that with the Final Fantasy games, pretty much the entire game is on every disc, except for the FMVs. On an actual PS1 you can take out the disc and put the wrong one in while you're playing the game and it will work up to the point it has to play an FMV. There might be some other stuff (maybe some background images) that's not on every disc though, I can't say I have tested every single part of them. The problem is this approach doesn't work for non-linear games. If you have a big game world that's too big to fit on a single disc, you don't want the player to have to switch discs every time they cross some arbitrary point in it. So some Xbox 360 games have an install disc and a play disc. Games don't directly use data from the disc. They load it into RAM first and use it from there. That's why you can switch discs at the appropriate point and the game keeps running. Everything loaded into RAM at that point is still relevant. The game is just coded to expect that it can't read anything from the disc while you're at the switch point.
