A user group makes managing permissions easier by gathering users into one group. For example, you might create a user group called "hr_users" and add user accounts for people in the human resources department. The existence of user groups isn't visible in the application's user interface.
User groups are made up of members and admins. Unless they have access to the Admin Console, members typically aren't aware that they're in a user group. The account simply defines (at least partly) their access to the application's features. Group admins have access to the area of the Admin Console through which they can manage settings and membership for a group they're administering. Unless they have other types of admin access, they'll only be able to access account management pages for the account they're administering.
Be sure to see Managing User Accounts and User Groups for overview information on how accounts work.