Curators are an unofficial designation. A curator is a community member who chooses to help maintain and cultivate the content on these sites. That is something that anyone can do, regardless of reputation, though it's easier to do with the privileges for editing and review. While editing and reviewing are two primary avenues for curation, they're not the only ones. Working on meta to define the scope of a site or to identify and remove tags that don't belong in the system are among a long list of work that we feel falls into the realm of the curator.
While asking and answering are integral elements of our sites, curation is necessary to keep the sites well-maintained and in good shape. We tend to find a progression in users that can stop at any of several points - asking/answering → curation (editing, reviewing, creating tag wikis, etc) → moderator. Many users may fall into more than one category but it's not uncommon for someone to focus on one area only.
Moderators are considered curators at a very high level. They have access to all of the tooling of curators (and often do some curation work) plus additional access to act to prevent damage to the system by users who have shown that they are struggling to use the curation tools as designed - for example, they have the ability to suspend users from review and block users with under 2k reputation from suggesting edits.
The work of the team focused on curators is to assist them in doing curation work more effectively. They may communicate with curators to identify issues with their workflows or improve existing functionality so that it better meets their needs. In general, we tend to consider much of the meta community, either here on MSE or on the per-site metas to be curators and we often communicate with curators through meta, for example, the recent announcements about changes we're making to the review system.