The public_html folder is not part of filezilla, but is the ROOT folder on your remote server (the one operated on a computer by your hosting company somewhere in the wide blue yonder).
All filezilla does is establish a LINK between YOUR computer, and the remote SERVER.
As you can see in filezilla, there are TWO "frames"...
One allows you to navigate to folders and files on YOUR machine...
The other frame allows you to navigate to folders and files on the REMOTE machine.
Then, the FTP functions allow you to send files to and from each machine.
If you have deleted / re-named / otherwise messed up the public_html folder, you may be able to restore it simply by correcting any edit you made to its name, or if you deleted it, create another folder and call it public_html
If you create a new public_html folder, it will be empty, so any programs/files/ folders that were in the original public_html folder will no longer be there, and you will have to restore them from your backup (you do have a backup, right) or re-FTP them from your hard drive.