The Public folder is a special folder (there's only one of it in the whole Dropbox. It's hard-coded) where if you put anything in you automatically get a link from which anybody around the web can view that file, without you having to explicitly click on the share button.
As is clearly stated on the page:
Dropbox accounts created after October 4, 2012, will not have a Public folder. Don't worry. You can quickly share anything with friends and colleagues—even if they don’t have Dropbox—by using a shared link.
So don't worry. It would be absolutely ridiculous to remove normal sharing function.
The removing of the Public folder is not restricted to free users. It's just that Dropbox decided to drop this functionality, for everybody.
I don't think there's anything that's very hard to understand about that statement. It's very clear. Maybe you got confused since you created your account after October 4, 2012 and don't know what the Public folder is.