They did this a few months ago. Its when they create more servers and take volunteers (there was an NPC you could talk to if you wanted to switch servers) and stick them in the new servers. I think they take people that didn't volunteer, but I'm not sure since it didn't happen to me.
They're not force migrating anyone, this happened back when the game was first released in NA. And as I remember, there were no new servers added either, which pissed quite some people off. So if anyone is thinking that new servers are coming, I seriously doubt it.
To clarify some more, you would migrate with all the items in your moghouse and on you I believe, all your gil and levels, etc. Your LS would of course be lost. I dunno about your rank or fame though, I have no clue what happened there. The real problem was that you couldn't pick your new server, you were randomly assigned a current server. And the Moogle wasn't just letting it happen to annoy, I think you needed to apply for it like marriage. Like I said before, I heard nothing of any new servers being made at that time, so if anyone has a server name, it would be useful.
I have 2 people in my friends list that moved over to the Shiva server. I can still see when they are online, but i cannot send them tells. Only messeges. I never cared to ask how they got there, cause have no intention of replacing what is most valuable in this game. Then people you deal with. But yeah i'll ask them about it.
One other problem with Server migration is your name. If there's a duplicate person applying as well and you end up on the same server by chance, someone has to change their name.
However, I'm sure S-E just wouldn't let you migrate. (but it's somewhere in the manual or something about it)