I'll try to explain it without getting that much into technical stuff. Sorry if it gets too technical

An url (web address) is basically formed by: subdomain.domain (Where the domain part is the name of the webserver(s) on the Internet).
So the Internet name of the webserver(s) that host this site is "halkomomoi.com". The sudomain for the forum is "forums". For the main site the subdomain is "www". So when someone types the forums.halkomomoi.com, the webserver answers with the forum part of the site. Also writting forums.halkomomoi.com helps keeping the URL short and that's why a subdomain is preffered.
Most people think that the www always go with an address, but it goes only when you want to access the main subdomain of the site. For example en.wikipedia.org doesn't come with the www, because you want to access the en (English) subdomain of the site.
If you want more information you can start with:
http://en.wikipedia.org/wiki/World_Wide_Web#WWW_prefix_in_Web_addresses