Public categories are a great way to have pages that are accessible outside of your organization.
All pages in a Public Category will be public to the world wide web.
You can view a demo account with public categories here.
Creating a Public Category
Click on Create a new category in the lefthand sidebar:
Now give your category a name, and change the Who should be able to view this category? to The Public.
Adding pages to public categories
All you need to do is create a new page, within your new public category, and that page will now be public to anyone outside of your organization. Or, you can move existing pages and subcategories into your public categories.
Changing existing categories to public categories
You can change an existing category into a public one by clicking the dropdown menu next to a category in the sidebar and selecting Edit:
Once you are on this page, change the "Who should be able to view this category?" to The Public.
Note: There is no way to have a Public Page in an Team-Only or Invite-Only Category. All pages in a public category will be public, and all pages in an invite-only category will only be accessible by invited users with a login.
If you'd like to share a single page outside your account without the viewer needing a login, try using a shared link.