TL;DR
Public file path is used for file uploads that happen in Drupal. Usually you want to use Drupal to manage content, that means article, users and files. This requires you to upload files inside Drupal application and this is where the public file setting comes into play.
Longer version
When you create a Drupal site, you can decide where all file uploads (which are public) should be located. The only rule is, that it have to be inside the webroot, so that they are accessible for download.
By default this is sites/default/files, but it could be /uploads or whatever you like.
This is used for when you actually use Drupal as a CMS and upload files on content like on articles, user profile pictures etc. When you upload files through Drupal and they are public, Drupal will save info about the file, know it's location and can do things with it.
Having the public path configurable is pretty smart, it means to change move or rename the upload folder and you only need you change one setting for it to work.
If you have FTP access you can upload any file to the webserver, it will be accessible to users etc. You should note that uploading files this way, means that Drupal wont know that they exist and can't actually use them in any way. It might be a good solution for your use case, but you are effectively bypassing Drupal as a CMS and if you plan on manually uploading all files through FTP, you will loose a lot of the file management features and the public file setting wont matter one bit.
Hope this clear things up for you a bit.
