Out of sync. It happens in multiplayer games. Essentially, at the end of each round, the game creates a checksum of the current game state on each computer that the game is running. The different PCs then compare their checksums with each other. In a normal game where everything is going fine, those checksums will be the same on each PC. When they aren't, you have an "OOS", and Out Of Sync error. It shows up as fat, ugly red text in the middle of the screen, blinking, and the checksums of all the players are next to their nicks in red as well, blinking too. At this point you must resolve the OOS somehow (playing on doesn't make sense--you can no longer be sure that what you are doing on your PC is what is happening on another PC).
To resolve an OOS, everyone who has a different checksum must rejoin, thus downloading the entire game again from the host. If the OOS is recurring, this solution doesn't make sense of course. If you have an OOS once every 200 turns or so, okay, I can see how you'd just rejoin and get on with it. But if you have to wait 2-3 minutes for a rejoin every 10 turns or so, the game becomes unplayable.
As far as I understand it, there are a number of reasons why an OOS can happen.
1) Random numbers. There's a getSorenRand function in Civ4 for that very reason: if there's something with a random outcome and each PC generates its own number, then of course different things will happen. That's why there's a function to make sure that each PC gets the same random number. Far as I understand it, this is pretty trivial and Kael and the gang surely are on top of this.
2) Differing game files. If I have a gamespeedinfo xml that says normal speed means science factor 100 while you, haxxor that you are, have made your own gamespeedinfo with a science factor of 20, then techs will research much quicker on your instance. One tech finishes on your PC while it's still researching on mine, bam, differing game states. Again, this is trivial: if no one is messing with his files and if everyone has the same game version installed, this should never be a problem.
3) Something happens that is not broadcast to other players. According to what Kael said in another thread, this is currently the most likely candidate. You see, when you move a unit, your game instance sends a message out to everyone else in the game saying "Player XY moved unit number 23 to plot (x, y)" or something like that, so all the other PCs can update their gamestate accordingly. If there's an activity, however, that doesn't broadcast itself, this could be causing an OOS as well (say Declare Nationality in a hidden nationality unit would for instance not broadcast itself to other players--so you'd declare nationality, and in your game that Hill Giant (are they still in? I forget ;P) is now one of your units, while on the other PCs it's still a hidden nationality unit. OOS)
OOS are very very hard to debug for a number of reasons. I think the biggest problem is that multiplayer savegames are next to useless. You can't go into worldedit with them, for instance, and to recreate the OOS you also need more than one PC (evidently).
Since I practically only play FFH multiplayer I'm very interested in seeing those OOSes resolved (as you can probably tell ;P)