As a community admin, you have control of certain things in your community. You have the ability to edit the community's name, photo, or description. If the community is private, you have the authority to accept or decline users requesting to join the group. If it is a moderated community, you have the ability to to approve or decline posts made my members before they are posted on the community feed.
If you are the one who has created the community, you are the owner of the community and you automatically have admin privileges. Any other admin must be promoted by the owner or other admins. All admins of a community can appoint new admins by going into the Members list of the community and pressing Promote below the user they wish to appoint. Any current admin can be demoted by clicking Kick under that user on the same page.