Group is a logical division of people and resources (learning and social content) in order to carry out a common goal. Groups can be created either by site administrators only or by any site member. The menu item Site Admin -> Create Group can be used to create a group inside a site.
Every site also has a default group which is auto created. And also, 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 member 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 or can be added or invited to join by group administrators (can be different than site administrators). Users can also request the memberships based on access level set for the Group.
Groups also support creation of sub-groups (when Org Hierarchy feature is on for the microsite). Sub groups are child groups under any specific group. You can create sub groups at any level. The user who is a member of a group is by default also becomes a member of parent groups. When a user is removed from a group, he/she is also removed automatically from all sub groups and all nested sub groups. Read more about Group Hierarchy here