I am abstaining from making a nomination (but the nominations made so far are great and the extra pair of hands would be very welcome as I have said elsewhere).
As Kitsune said, the best place to look for information about what moderators do is the "A Theory of Moderation" blog post.
I thought would add, more informally (and somewhat belatedly), some notes about what moderating this site is like.
We come to the site regularly to check if there is any tidying up to be done. Mostly, that means that a lot of the times that I come here I will just be busy with the invisible work of addressing flags (deleting bad posts, converting answers to comments, deleting yet another account from everyone's favorite resident troll). From the mod control panel it looks like jmbejara and I have made about 500 interventions in the last quarter, most of them extremely minor. I try to exercise a light-touch approach and let the community deal with as much as possible (e.g., though voting).
This work naturally takes away some time that might otherwise be available for writing answers on the site. But I try to keep an eye out, in particular, for questions where it looks like I might be well-placed to make a pivotal intervention.
It's useful to keep an eye on what the other moderators are up to. Sometimes, a moderator will be away and it is then necessary to increase the frequency of your own contributions to prevent flags from piling up. But even then, the site never demands more than about an hour a day.
Sometimes, moderation requires coordination with other sites (e.g, because we need to check whether they are happy to receive a migration, or because we need to check whether a suspicious econ user also looks dodgy on other parts of the network). For that purpose we have a special moderator chat room (called "Teacher's Lounge"), which is also a good place to talk to more experienced mods about any questions we might have.
It's useful to also spend time reading about how the SE network works more generally (e.g., by browsing the help documentation, blog posts, and meta.stackexchange.com) because people often have requests/questions that boil-down to network-level rather than site-level policy, and because this knowledge is helpful when dealing with new situations for the first time.
I try to contribute to any issues that show-up here in meta. I think that being singled-out as a moderator inevitably lends a bit of extra gravity to interventions on topics like site policy. So I consider it important to reflect on the evolving nature of the community and the ways in which it might be prodded in the right direction.
If anyone has any specific questions, I'd be more than happy to offer my perspective.
Kitsune Cavalry asks: "how much communication [do] you have with the community staff and what [do] the discussions entail"?
The answer is, very little. In fact, in the three years that the site has been up and running I can only remember two occasions on which it was necessary to communicate with the team. The first was for some guidance on how to deal with a particularly problematic user; the second was recently to discuss the need for extra moderation help on this site. In both cases, the team was very responsive and supportive, and one has the real sense that they are there to help whenever needed. But at the same time, the network gives moderators a pretty comprehensive set of tools, which allows the site to be fairly autonomous.