Moderation is used for limiting postings that are sent out through the mailing list. While most lists are unmoderated, some owners want to review postings and approve them before they are sent to list members, which requires moderation.
Generally the owner(s) and moderator(s) of a moderated list are the same, but non-owner moderator(s), who can moderate postings but not change other configurations, can be added by the owner.
To allow anyone to post to a moderated list without requiring approval, the steps in both Allowing a member of the list to post on a moderated list without requiring approval and Allowing a non-member of the list to post on a moderated list without requiring approval, above, must be applied.
See How to Turn on Emergency Moderation for a List