The term "community manager" is perhaps a misnomer. A better term might be "community supporter." We have a community manager/supporter at RethinkDB, and here is what Christina does:

  - Proactively reaches out to users to see if they need help, then
    connects them to the developers on the team in case they need
    something but haven't reached out themselves (which is
    surprisingly common).
  - Searches for meetups related to our product/company and helps
    meetup organizers by sending them gifts for the attendees,
    gives them occasional food budget, organizational advice, etc.
  - Organizes our own meetups and makes sure food, drinks, label
    printer, venue, and a million other things that go into events
    are all set up and ready to go for the attendees.
  - When she notices community members are working on related
    projects, she acts as a network hub and connects them to each
    other.
  - A million other things that need to get done when you have a
    large, distributed, non-hierarchical group of people trying to
    accomplish something.

We use the term "community manager" because that's what the industry standardized on, but really she's not managing anything. She supports the community in every way she can, so really, she's a "community supporter". It's a vital role, and every good open-source project has someone doing the job, though they may not necessarily have an explicit title.