Discussion boards are a platform for hosting online interactions between people who wish to discuss the aspects of particular topics of mutual interest.
At The Motley Fool, for instance, there are many discussion boards devoted to a multitude of various topics. These include (among other things) art, personal finance, travel, religion, general investing, investing in specific company stocks (such as Apple or Zhongpin, Inc. -- and just about everything in between), retirement, etc.
Of these, there are "public" boards, which are open to anyone having access to the internet, and there are "subscription-only" discussion boards, open only to subscribers of the Motley Fool newsletter that "hosts" those particular boards.
The Motley Fool public discussion boards are available in a read-only format to anyone wishing to access them. However, only registered users may create new posts or polls, and post responses to existing posts. Unless a person subscribes to a Motley Fool newsletter, the ability to become a registered user is only available by invitation from an existing member (with some exceptions). The theory behind this distinction is that having some restrictions in place will help to maintain a higher caliber of discussion.
At The Motley Fool, the aim is to educate, enrich and amuse. The discussion boards endeavor to reflect that in the content provided. Humans being human, that high ideal isn't always achieved, but it is an ideal for which the general posting community strives and -- more often than not -- achieves.