Facebook Groups is a great way to chill online with friends who have similar interests /activities /beliefs as yours. Groups are for fun and general entertainment. FanPages are more for commercial uses (Large groups, Commercial Brands, Internet Marketing, etc)
Groups can be a useful way to interact with multiple people at once. You might set up a Group to reconnect with your college buds, talk about certain political issues, plan an event or party, or communicate with members of a club.
To Create a New Group: In the left pane of the home page, click Create Group.
The Create Group dialog box will appear. Enter a name for your Group in the Group Name box. Add Group members by typing the names of the people you wish to include in the Group Members box. You can only add people who are already your Facebook Friends.
Choose the privacy settings for your Group. There are three options: Open: Anyone can view the Group, its members, and their posts. Closed: Anyone can view the Group and its members, but only members can see Group posts. Secret: Only members can see the Group or any of its information. People who are not members won't even be able to see that the Group exists.
When you're satisfied with your Group settings, click Create. The Group will be created. If you are looking to learn how to make Money on the Internet, then check out this New Facebook group I just set up.
"Facebook Tips: Facebook Groups "
Reference : facebook101tipstricks.com