Groups are most often created to provide training to functional groups such as Haz-Mat or Dive Team. Another example would be training by shift at career departments where you could create separate assignments for Shift A, Shift B, etc.
Creating Groups in the Academy can allow you to better manage subsets of individuals, and assign Admins within your Organization to oversee the users in the Group they own.
When you assign an Admin to oversee a Group, that Admin can only manage those users and perform actions for that subset of users, such as generating Reports and creating Assignments.
The most common use case is for when a medium or large Organization has multiple Divisions that each have their own manager or someone who oversees training for that Division. This allows Organizational Admins to delegate to Divisional Admins so each Divisional Admin can manage their own Division's set of Members.