A Facebook group is a page created for an organization or business to promote activities. Users can join the group and post their thoughts on a wall and interact through discussion threads. While Facebook groups were the main way for businesses to bring users together and have discussions for many years, the introduction of fan pages (which later became "like" pages) in 2007 changed this.
Though similar, groups and pages offer businesses and organizations different ways of reaching their audience. Mainly, fan pages have the advantage of being able to display information directly into their fans' news feeds, while groups cannot. Pages also tend to have higher Search Engine Optimization (SEO) opportunities than groups. Groups, however, have the ability to message their members, as well as restrict who can and cannot join.
Nick O'Neill explains the main differences between groups and fan pages.
Facebook Help Centre answers frequently asked questions about Facebook groups.