Sharepoint - Office 365 Public CDN - What does the Public actually mean?

"public" means that technically files are available anonymously through the CDN URLs. There is referrer filtering, which will block Office 365 CDN to be used as the hosting location for assets which are not used in SharePoint.

It's important to notice that you will only expose static assets like JS files or images, not actual content. Only those which are located in the CDN origins.

If you use Public CDN option, there's no automatic URL rewrite.

If you, however, take advantage of the private CDN option, there are other differences as private CDN is only for authenticated users and URL rewriting happens automatically. Private CDN though means also that the CDN URL to assets is not static and keeps changing automatically.

Hopefully that clarified things a bit.