Here's an explanation of what will happen:
The content will be hosted on 2 seperate servers and the DNS will be changed to point towards the new server. This is a change that has to individually go out to all your internet service providers (ISP). The amount of time it takes for this to occur depends on your ISP, so it will be different for everyone.
I will have to close the forums on the old server. The reason for this is because anything you might post or change on the old server would be lost after the move is complete. So, if you visit the site tomorrow or Saturday and the forums are closed, your ISP hasn't updated yet. Give them some time and try again later. Once you see an active forum, you'll know you're looking at the right place.