Torn is right. But there are also larger administrative purposes.
User groups allow us admins to give certain individuals certain privilages. For example, once you've been verified as 18+, you get to be added to that usergroup, which allows you access to the Classified forums. The verifiers themselves have their own group which gives them access to discussion forums for that purpose.
On a very simplified basis, you are moved automatically from one usergroup to another after you verify your email address when you sign up, and that's what allows you to post, as opposed to having limited access prior to that.
Most usergroups you won't be able to join if you tried, simply because they are locked and invite/admin controlled only.