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. 

Creating a Public Category

Head over to the All categories  page (can find this in the top left menu dropdown),
then click Create a category

 Now give your category a name, and change the Who should be able to view this category? to The Public.

A little message will show warning you that all pages within this category will become public.

Creating a Public Page
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. 

Making a Private Category Public
 It is also possible to change an existing category into a public one, to do so, click on the name of the category in the left menu drop down on any page, and once on the category page, click "Edit category" from the small dropdown on the right:

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 a Private/Team Category. All pages in a public category will be public, and all pages in a private category will be private.

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