Forum links building is way of getting backlinks from forums. Some forums allow members to place their URL as signature. These links gives a SEO benefit. Forum link building directly help to increase SERP. I know this because of my experience in forum link building.
The reply from linkgenie describes it well enough. And i agree that is sueful and worth while. it helped a number of sites I have worked on, and even got me a few hundred direct visitors each month, which was cool. I always say though, these things are only effective when usedwith other things. So don't rely on forum posting alone, mix it up with a few oter backlink building strategies and techniques.