Group is a logical division of people and resources (learning and social content) in order to achieve out a common goal. Groups can be created either by site administrators only or by any site member. The menu item Group -> Create Group can be used to create a group inside a site.
Every site also has a default group that is auto-created. In advanced usages, a group can be shared by more than one site if required.
Every member in a group has a role - admin, instructor, or learner. Apart from this, each group has one Owner. Users can be members of multiple groups, where they can have different roles. This allows setting up individual controls and authorization easily to meet the needs of any organization.
Site members can join a group on their own, can be added or invited to join by group administrators (group administrators may or may not be different from site administrators). Users can also request the memberships based on access level set for the Group.
Groups also support the creation of sub-groups (when Org Hierarchy feature is enabled for the microsite). Subgroups are child groups under any specific group. You can create subgroups at any level. The user who is a member of a group is by default a member of the parent groups. When a user is removed from a group, he/she is also removed automatically from all subgroups and all nested subgroups. Read more about Group Hierarchy here