Double turns
It is possible to take a 'double turn' in the game by being the last to finish for one turn and then the first to finish the one after that. This has a positive effect because it speeds the game up, but the downside is that it can be exploited for military advantage by moving twice before your opponent has a chance to react.
So to keep the upside of double turns while eliminating (or at least minimizing) the downside, the rule is that if you are at war with another player (or are about to go to war with them, eg. sneak attacks) then you mustn't take two turns before they've had a chance to take one, or in other words you cannot go after them in one turn and before them in the next.
You can use the civstats log page for the game, or the RSS feeds from the same page, to tell if the other player has taken their turn (ask me about this if you don't know what I'm talking about).
One exception: you may always take your turn when 12 hours have passed on the turn timer (since the timer seems to run slow this will probably be a bit more than 12 real hours), regardless of whether they have taken their turn or not, otherwise it'd risk you not having a chance to take your turn at all. Ideally though, you should talk to your opponent(s) and come to an arrangement about the order you are going to take your turns in.