Private society forums are now offered only after a society has first created a private forum Group and used that for several months. If the society 'outgrows' the capabilities of the forum Group system, transition to a private society forum can be requested.
When creating the society forum Group, the creator has the option of making the Group public, private (new members must be approved by the Group owner), or invite-only. This setting will determine who is able to join the group, and who can view content posted within the group (i.e. discussions, group images, etc.).