The world hasn't DRASTICALLY changed in terms of technology. The politics are a little shifted. I should have plotted this all out before I asked for character sheets, but I was sort of caught off guard by how popular this idea is.
Simply put, Galbadia is passive these days, trying to rebuild their might after the losses the suffered during the game. They're trying to hold firmly onto the city of Timber though, largely for morale. As long as they hold on to at least Timber, they can tell themselves they've still got some of their great empire.
Timber itself is resisting, with a new, more militant Forest Owls (Imagine the difference between Final Fantasy 7's AVALANCHE, and Before Crisis' AVALANCHE, and that's pretty much what the Forest Owls are like now), and the city is in something of a civil war.
Esthar is still struggling to fix the damage from the Lunar Cry, with monsters still being a major and constant threat within the city, and repairs still being carried out.
Dollet has been independent now, and there have been shifts in the inner policies. There are rumors abound that the Duke of Dollet is in possession of some sort of great power, but no evidence to back up the claims have been found. All the same, it has lead to political tension between Dollet and Galbadia, with the Duke of Dollet insisting Galbadia is spreading the rumors to turn everyone on Dollet, while Galbadia builds back up its forces to resume a campaign of conquest.
FH is still pretty much the same. Its one of the few places left that's peaceful and without any sort of political tension with anyone else.
Balamb is the same, though there was an attack a few years prior to the start of the rp, where a group of rogue Galbadian soldiers attacked the town, blaming Balamb for Galbadia's problems. This has left the people of Balamb mistrusting of Galbadia. It was during this brief conflict, that Yuge earned his reputation as both a ruthless monster, and a brave comrade-in-arms to his fellow SeeDs.
Trabia is... Trabia. Its cold and snowy, and pretty much everyone but Trabians and the Moomba don't care too much about it xD Trabia Garden is still working on repairs, trying to fix the Garden's internal systems.
Galbadia Garden is still struggling with PR problems after their association with the Sorceress. That said, however, they've been nothing but cooperative with their fellow Gardens since the game.
Balamb Garden has stationed SeeDs at both other Gardens to help with repairs and maintain the peace. These SeeDs still answer to Balamb Garden above Galbadia and Trabia, however, though they are encouraged to cooperate with the locals, and help promote friendly relations.
Winhill... still pretty much just a lovely little town out in the middle of nowhere.
... did I forget anything?