We believe deeply in community moderation. That's why we appoint Pro Tempore Moderators and, ideally, democratically elected community moderators for every site in our network. But what do community moderators do? The short answer is, as little as possible!
@AditKirtani They have a great number of powers, as indicated here.
Virtually all moderator actions are binding: closing, deleting, approving tag synonyms, you name it. The moderator's decision takes effect with a single vote.
They also can take special actions, such as merging two very similar questions, locking controversial questions.
The main duty of a moderator is too handle flags, which ordinary users put up.
Users may flag posts for a variety of issues, such as not answering the question posed, being commerical spam, overtly offensive, or other issues. Moderators will see these flags and take appropriate action.
Moderators also handle comment flags, which are similar: obsolete, offensive, and so forth.
2016 Puzzling Moderator Election
2016 Puzzling Moderator Election