So, what it does is, like any FB app/game - it associates your FB account with this forum account.
If you wonder how others see your account after you connect, look at mine: it is currently connected.
(You can see it in my profile)
Once you connect, you have the option to share links and recommend/like threads.
post directly to your FB feed
share the site
convert your forum avatar to import your FB avatar
view/post to FB live stream
see who has recommended the site and pages (and make your own)
view FB stuff form inside the forum:
there are also some settings in your profile
Enable Post To Wall prompt when logging in with Facebook Connect: Facebook Profile Badges
Show Facebook Profile Badge in Profile:
Show Facebook Profile Badge With Signiture In Post:
for new users, they can semi-automatically set up a user account on the forum using their FB login.
And finally... if you don't like it, there is a "disassociate" link in the profile which turns OFF the connect.