If you want to get a real insight into the daily work of the moderators, the moderator newsletter is available to everyone. It talks about all of the new features, changes in policy and so on.
The site get more features the more reputation you earn. To a moderator, the site looks more or less like it does to a user with 10,000 reputation.
At the top of the page, there are two notification bubbles for Moderator Flags and Pending Edits:
The mod
link point to the Moderator Tools, And the tools
link is the same as the 10K tools.
In the moderation tools, we can do various janitorial things. There are some interfaces for things like System Messages (the messages you see atop every page sometimes, like when there's an election), merging user accounts, and creating tag synonyms. And that's pretty much all of the stuff we use.
At the bottom of every answer, the links are the same as they are for a 10K user, plus a mod
item where we can Merge questions, protect them, convert answers to comments and so on.
As you can see, apart from the ability to actually affirm or invalidate moderator flags, plus some small things like the ability to email users directly, 10K users can do pretty much the same things.
Remember that we spend 90% of the time on the Flags page (which looks just like the 10K flag page at tools → flags). Clicking on a question, sorting it out (i.e. deleting an answer, adding a comment, downvoting, upvoting, ...) and repeating that process until there are no more flags left (for about 20 seconds).