The admins usually are busy organizing, handling that advertising and roadmap, doing backups and upgrades, etc. Why not outsource that to the tech guy? Both the admins and tech guys aren't suitable for putting on that smile and keeping track what goes on in a community - not always at least, especially when the board gets bigger.
If you have a person that site in between the top guys and the regulars .. you have a go to point. The collected info and what's trending on a site can be caught on to early, such as mods abusing status, or regulars ready to revolt, or other nasty things. Being there to be an objective voice to the users, the team and the admin .. data can flow both ways and the admin can stay on top, the team in tune, and the regulars feel more welcome and listened to.
The community manager doesn't have to be there 24/7, but frequently does help. The modding of a community can be left to the mods, the running of the site to the admins .. Communication and discussing matter that need the admin or user attention can go through the community manager.
A CM can mean a lot of different things, depending if you are a company, a hobby site, a software / product site with a support forum (or say a Sony online community) to big corporations with verticals. etc. The role and expterise changes, along with the position and paycheck.
But it allows the admin to focus on what is important. the team to focus on the content and users, and the users having a friendly smile to talk to for simple to complex questions, feedback or complaints.
The CM can have more access to inside info, allowing them to make better decisions knowing the inner wheels of a community or company. Which helps with decision making thinking through public face, the future, upcoming announcements etc .. sometimes "just" a moderator might go "dont talk back to me! BAN" .. not realizing somethign else might be up. A nasty situation that could have been prevented with better communication.
Let the mods moderate, and the CM write out the policies explaining situations that happen on the site as training material for the mods to do a better job. Let the tech guy configure the setup to please the team and the users with a balanced setup of a board. While the admin just signs off on things, or gives the freedom to let the team, tech ppl and the CM play within the board-boundaries.
Not every community needs all of this, but if you want a great community you have to at least consider what might and might not work for you - how you address it and how it could help you now and in the future.