Good-Of-The-Order

It probably refers to "orders" such as The Order of St Francis, or The Order of Elks. These are religious or social groups with a relatively "closed" membership. "For the good of the order" means for the benefit of this organization (sometimes at the expense of certain individual members).

http://www.calltoorder.us/FAQ/Goodoftheorder.html

Question: In a meeting, what is the president asking for when she asks "Is there anything for the good of the order?"

Answer: [...] According to Robert's Rules of Order, (See https://en.wikipedia.org/wiki/Robert%27s_Rules_of_Order) Newly Revised 10th ed. (RONR), the term Good of the Order refers to that portion of the agenda or meeting during which members may make statements or offer observations about the character or work of the organization without having any particular item of business before the meeting. That is, under normal circumstances, members of a meeting are allowed to speak on business matters associated with an agenda such as a report of an officer or committee of the organization, or making a motion and speaking in favor or in opposition to a motion. Under the agenda heading Good of the Order, however, no particular business needs to be at hand in order for members to make statements relating to the organization.