When granted moderator status in a community you are authorized to do the following,
A settings button should appear right above the listed members on the right hand side. From here you will have access to the following settings.
Add another community member as a moderator. Under the Moderators tab.
Edit Topics Settings. Under the Topics tab.
Invite new people to join your community. Under the Invite tab.
Approve or Deny member requests. Under Join Requests.
Edit affiliated groups. Under Related Groups.
Delete your Group
When clicking the three dots on the top right of any post in your community. You will now have three additional options.
"Pin" Which pins the post to the top of the community stream.
"Flag" for inappropriate content which marks it for review.
"Remove from community" which removes the post.
Click on members, then the three dot menu on the top right of any person. You will then have the option to remove this person from the community.
Create an Announcement
Create an announcement on a post using the megaphone icon at the bottom. An announcement makes the post go out as an email and push notification to all members of the group.