In the web site frontend, Joomla has NO standard support of registering different users in different groups. If you want to give your users the ability to choose their own group, you must use JGroup.
Suppose, for example, having to make a site for a school with different content for each calss of pupils. Each user must necessarily be able to indicate, when registering, his belonging to the class A or B, etc. .. Only in this way you can see the contents of your class.
In many other cases you may have need to show groups in the registration form.
JGroup: what allows you to do
1 Choice of groups to show in the registration form
2 Manage the association of the user with multiple groups in the registration form
3 Make it compulsory or not the choice of group (groups if you choose the multiple type)
4 Show, in the frontend profile view, the name of the groups selected in the registration phase
5 Allow user (or not) to change his group (groups) in the frontend profile view (edit button)