I hope all the questions means you're feeling better!
I can only guess what administrators do, so let's call it magic. Moderators, from my view, keep the conversation going, and try to make/keep dance forums a fun place to be. There's more, but these are the goals I see.
The moderators are all responsible, as Jenn, says for trying to keep their forums running smoothly. As part of this role they also have the ability to move posts, split them, edit them and, if needed, delete them in the forum(s) that they moderate for. On the whole we try to intervene as little as possible, but it’s basically the moderators who oversee that the forum guidelines are being followed. You can see who the moderators are, listed next to each of the individual forums.
Ok, as for administrators, well, DanceMentor is the site administrator, which means that he's the technical guru behind Dance Forums (Yay DanceMentor!). Technically I have administrative status too, which means that – in brief – we can both moderate any forum as well as change any of the set ups (such as the recent shift in rank names/posts) as needed.