With public folder feature, dropbox allowed their users to host a static site in a very easy way, instead of buying hosting, using FTP and so on.
With public folder every file inside has direct download link. You can embed images or simply create direct links to your files (put signatures in forums, pictures)
Public files are so simple; it works like a file server, but without having to run a file server on your home computer. Things in the public folder are viewable; things outside are not.
Dropbox disabled these feature with no official reasons, rumors say it’s because of massive bandwidth usage and copyright issues.