Organizations is an OEM feature that allows you to define user organizations and assign users (local & Single Sign-On) to the organizations. You can define report folder privileges per organization. You can also have user groups with the same name among the user organizations and give privileges based on organization, organization+group, and per group. This will help manage the privileges in multi-organization installations.
You can define the permissions by the organization, by group, or by an organization and the group.
User organizations have two fields: name and external ID. The external ID is the ID that is passed in from Single Sign-On server. See Single Sign-On (SSO) / User organization with SSO for details.