New members' first three posts and replies wait here, and so does text that other accounts posted word for word. Approving one makes it live and counts toward the member's three; after three they post straight away. Trusting a member approves everything of theirs that is waiting.
Site mods can do what the site owner can across the whole site: run every community and its live chat, pick and remove community moderators, and use this page. Only the site owner can add or remove site mods or give a community a new owner.