An owner will be able to:

Add and edit categories ( a category is a new page)

Remove posts Remove members from the community Ban members from the community

A moderator will be able to do everything an owner can do to manage the community except add additional moderators and delete the community.

Google communities

your private community posts will only be visible to people in those communities

the posts you share to a private community will not show up in your friends and followers’ Home streams (on Google+) unless your friends and followers are also members of the same community.

Default – posts to the private community show up on your own Google+ home page UNLESS you adjust YOUR settings in that public community for them not to show.

You can turn your community notifications on or off by clicking on the icon on a community’s page

A community’s privacy settings currently can’t be changed once it’s been creatednames of communities do not have to be unique (other communities can have the same name)

You can change the name or the description of your community via "edit community" accessible by clicking on the settings wheel

Add new categories (i.e. a new page) by selecting Edit community from the Actions menu.

Click on the discussion category before writing in the box "share whats new" i.e. before starting a new thread.

Starting a new thread on the "all posts" page will only appear on the all posts page. A new thread added on a "categories" page will also appear on the "all posts" page.

Categories can be added, re-named, re-ordered, and even deleted easily

Only owners and moderators can start new categories.Add moderators to your community

You can "invite people to join" or when setting up the community choose the option "Let people find through search and request to join"

See privacy options here https://support.google.com/plus/answer/2872671?hl=en