There are currently ten people on this Team. In order of hire date they are:
What do they do?
The Community Management Team is part of the broader "Community Team", the staff members focused on the needs of the Stack Exchange communities and the strategy and planning for community initiatives. You can read more about the entire team in this post.
Explaining the breadth of what the CMs do is complicated and difficult to enumerate, but here are some of the things they've done and continue to do over the years:
They help you out. No, really. But yeah, that's about the most generic non-answer ever.
They review proposed sites passing through Area 51, revising, raising concerns, closing, destroying, and preparing for their launch as the situation warrants.
They moderate brand new sites as they launch, answer questions and attempt to communicate lessons learned on past sites. They run the process to obtain the initial set of Pro Tem mods, and hand the site off to them.
They're the navel of the SE administrators, always available for gazing.
They watch the various and sundry meta sites, answer questions, address or escalate requests and provide guidance in the use of the site's tools.
They occasionally answer emails.
They review moderator actions, offer advice, resolve disputes.
Now and then, they sleep. One eye open. Like birds.
Are they moderators?
While CMs hold moderator privileges on every network site and much of their work touches on moderation, they are not part of the site moderator teams. No elected or appointed moderator is an employee of the company, while all CMs are. Some have gone from moderator -> employee and vice versa, but the orange "Staff" badges on their pages indicate clearly if they work for the company. If you're curious about who has made that switch, it's documented here.
No, they are not. That is a special user that even has its own tag, community-user.