I am not too great at this either and yes, I know that the mods most probably do much more than what I may list down but here goes anyway, until someone contributes a better explanation.
A mod is like a supervisor. S/He makes sure that everything is done properly in the forum, because the admins cannot always be there to correct mistakes or spot them or warn people around them. So the moderators help the admins to do that, I guess.
You usually see Yavannah or malary for example, editing the posts of those spamming the download section and they give them a warning if they sees that a warning must be given. This is an example of how a moderator 'moderates' things around here in the forum and makes sure that the rules are followed.
Moreover, a moderator here has the power to ban someone, if they see that they should be banned. A moderator can edit/delete/move/merge posts and threads (they can open/close those too), which furthermore means that s/he enforce the forum rules.
To make a long story short...a moderator's job is to simply enforce the forum's rules. Or as you put it...'all that jazz'
I hope someone better comes along to explain
Donna...