Moderators are forum participants who are responsible for keeping order. They may have capabilities within the forum greater than those of other participants: for example, they can sometimes add new participants and suspend people who are abusive. They also work to keep the discussions friendly and relevant to the forum.
A forum with a moderator is said to be moderated. Forums without moderators are unmoderated and are generally places where newcomers should tread very carefully. Moderators tend to introduce themselves early on in forum discussions, so it’s usually clear whether a forum is moderated or not.