You have alot of incoming links - about 4000 or so, so it seems to be
quite a popular site.

If you just move the forum to a new folder, you will find some of
those links are going to return 404 errors - ie, they will become
pretty much useless - people won't be able to find the pages anymore
from those links, and neither will google, so you could see a big
pagerank drop.

It's generally not a good idea to move an established page to a new
subdirectory unless you absolutely have to, for that reason.

Here are a few options:-

1. Find something similar about all the moved pages - for example, I
see that most of your pages start with showthread= ... you can use mod
rewrite to 301 redirect these pages to your new subdirectory - a 301
redirect seamlessly redirects people coming in via an out of date link
to the new correct link.

This approach may be a little bit technically difficult, and if you
choose to do it, you probably should employ someone knowedgeable to do
it for you. A good guide is here -

http://httpd.apache.org/docs/2.0/misc/rewriteguide.html

2. My suggestion if you really want to make this new site a distinct
entity - First make your new site in a subdirectory of your existing
site, link to it from your first page so that it gets all the Page Ranking
benefits (regular crawls etc) of your existing site, and also lets
your users know about it.

Wait about a month or so until it is well indexed and is getting
traffic, and then 301 redirect that whole subdirectory to a new
subdomain - eg newsite.zerovb.com