We implemented this new role a couple of months ago and are finding it very useful. Here at Bellevue, we actually have replaced OrgMembersOnly with OrgLeadersOnly for our lay leaders. Assigning this role to your lay leaders allows you to give users more privileges (like Edit or Attendance), because they are limited to only those Organizations in which they are a Leader. Whereas, with OrgMembersOnly, they have access to every Organization in which they are enrolled regardless of their Member Type in the Organization. Read more about lay leader user roles.
Another new feature that goes hand-in-hand with this new role is the concept of Parent/Child relationships for Organizations. The purpose of these is to give a lay leader (who has OrgLeadersOnly role) assess to Organizations in which he is not enrolled. Read more about these special types of Organizations.