When it comes to LEGO fandom there are two meanings of community. The word has been used as a catch-all term for everyone involved in any way with LEGO as a fan whether they be a collector, builder, seller etc. The term is also used to describe sub-sets of AFOLs, primarily online using message boards, Flickr group or other internet-based media.
World Wide Community
Sometimes used in a negative context (ie: communitarian) the concept of a world-wide LEGO community is based on the idea that anyone who loves the brick is part of something. This concept has even been extended to those people who work for LEGO whether that were self-described fans before being employed.
A community in this context is most often an online place where people hang out and discuss things, often, but not always a particular topic or branch of the hobby.
Some of these examples are also organizations, but not all are. Some but not all organizations are communities (organizations that don't host discussion aren't.)
A community may be open (anyone can post) or closed (only members can post, or in some cases only members can read) and it is useful to denote which it is.