What the heck is a migration?
From Meta SE:
Migration allows an off-topic question to be moved to another site in the Stack Exchange network gracefully. It preserves the current revision of the question, all its answers, and any comments on any of those posts, as well as most of the votes.
If a question is on another site where it is off-topic, it can be migrated to a place where it is on-topic, in hope that it will get answers to help the author.
Most of the post is retained when a post is migrated between sites. There are a few things that change though...
Downvotes are cleared
Since many off-topic posts can attract down votes, the down votes are cleared when a post is migrated. However, upvotes stay with the post when migrated.
The question, along with all answers are migrated
When a post is migrated, the question moves, as well as the answers associated with it.
The users don't delete their accounts, they just don't have an account
This is a confusion that seemed to be more common: On the original site where the post was created, it will look more like this:
But when a post is migrated, it may look more like this:
Why is this?
Good question. This happens when the author of the post does not have an account where the question was migrated. When this happens, the link is simply deactivated because it will point to nowhere. If the user does have an account, or creates one afterwards, the post will be reassigned to the new account.
How do I know if a post is migrated?
Most posts will have a banner below the question that looks like this:
This banner is pretty neat: It will tell you from where the post came from, and at what time.
In fact, if you look closely, this question was originally posted on the main site. But, obviously, it's off-topic, so it got migrated here :)
Keep in mind that since this is a beta site, migrations will have to be initiated by moderators, and moderators only. Generally, moderators who migrate here have a good understanding of what is on-topic here. But, most migrations will go through your 3 site moderators, so you can be sure that most things will be good, and that we'll fix up the minor things when it comes.
What if I don't like a migration?
That's fine. No one says that you had to accept anything. In most cases, there are many things that community members can do if they don't like a post. In these cases, you can reject migrations.
If a post is off-topic, or just deserves to be closed, vote to close.
Treat it like a normal question. Don't like it? Flag/vote to close. When the post gets closed, it will reject the migration.
Flag for moderator attention
Want quick attention? This will allow us to take a serious look at the post, and to see if we can salvage it for the site. It will also alert us to see whether we can get into contact with the users, or with the moderators who migrated the post. Whatever the case is, we'll work it out :)
What is a rejected migration?
I'll just quote good ol' meta again:
A question can also be rejected by the target community after it has already been migrated if it gets closed as a reason other than duplicate, or gets deleted (usually by the owner) on the target site. When a question which was already migrated gets rejected, the entire process of the migration is reversed.
Any sort of post that has been migrated can't be migrated to another site again, so keep that in mind. We don't want to be throwing posts around the entire network :)
Basically, migrations are just a way to move posts around to help askers get the answers they seek. Nothing much more to it, and you as a community are here to help, no matter where they come from. :)