What Does Facebook Group Mean?
A Facebook group is a page that any Facebook user can create that others can join, allowing group members to interact based on a common interest, affiliation or association. Facebook groups may be open to anyone, or joined by invitation only. A Facebook group allows members to create a community by promoting, sharing and discussing common topics.
Although the functionality to create groups on Facebook still exists, Facebook pages are now promoted as a similar application with more interactive options.
Techopedia Explains Facebook Group
Facebook groups run the gamut from sports teams and nonprofit organizations to random interest groups such as "I Love Peanut Butter and Jelly" or "If You Don’t Start Walking Faster, I Am Going To Hit You With My Backpack." Groups notify group members when new posts are added to the group page's wall. However, groups lack the functionality of the newer Facebook pages, which are able to display posted information on members' (or "fans'") news feeds. Pages are also better optimized for search engines and provide a much greater ability for administrators to customize the page. As such, while groups are still used for personal interaction, pages have become popular with businesses looking to advertise to and interact with their customers.