This applies to Social Feed, Announcements and Crowd Pics pages. They are the same page type, and this is one of the settings that differs between them.
The two options
Everyone — anyone who has your app can post.
Admins only — only you and the team members you have invited can post. Everyone else reads.
Changing it
Click the gear icon next to the page in the Editor's page list, and set "Who can post?". Publish your app afterwards, so the change reaches people who already have it.
Which pages start out as what
Social Feed and Crowd Pics start as everyone.
Announcements starts as admins only.
Why you might restrict a page
Admins-only is the right setting when a page carries things people need to find quickly — travel changes, room moves, timings. If anyone can post, important updates get mixed in with the conversation and an attendee scrolling for the bus time has to hunt for it.
That is why an Announcements page starts out admins-only, and it is worth leaving it that way. If you also want somewhere your attendees can post, add a second page for it. Running one admins-only page for updates alongside an open page for conversation works better than one page trying to do both.
Opening up a page
If you have a Social Feed page you set to admins only and now want it open, switch it back to everyone. Bear in mind that people will need to identify themselves before they can post — see sign-in and privacy on social feed pages.
Posting happens in the app
Whoever can post, they post from the Yapp app on a phone or tablet. There is no way to write a post from the online editor. See posting to a social feed or Crowd Pics page.
Reference
Social Feed moderation — approving posts before they appear, on a Team plan