The folder /home/username/public_ftp/ is used by the FTP server to store files for the “anonymous” users. Anonymous users are users that connect to the FTP server with the “anonymous” username. They don’t need to have a password.
Notice that you have a similar folder in your account /public_html/ – this folder stores the site’s content that is available for the public. Do not delete this folder.
For security reasons, anonymous FTP is disabled on most of the shared and reseller servers. Ask your host for more details.