Back in March, Dropbox made the decision to remove Public Folders for free users and in October, made it impossible to use HTML content in shared links. Dropbox will continue this lockdown next year, when it shuts off Public Folders for paying users also.
For free users, Public Folders haven't been around since late 2012, so this only really affects Pro and Business users. Dropbox's plans for the feature can be found on this help article:
As of October 3, 2016, you can no longer use shared links to render HTML content in a web browser. If you created a website that directly displays HTML content from your Dropbox, it will no longer render in the browser. The HTML content itself will still remain in your Dropbox and can be shared. Learn more.
Dropbox Pro and Business users: Beginning September 1, 2017, you can no longer render HTML content and the Public folder and its sharing functionality will be disabled.
As gHacks' Martin Brinkmann notes, Public Folders have been used extensively to embed images and other content in forums where such functionality doesn't exist. While users will find other ways to do this once the feature goes away, it doesn't help all the existing content currently being hosted in this fashion.
Fortunately, with the cutoff date being September next year, there's plenty of time to sort out another option. I have no doubt Dropbox will send warnings leading up to the date so no one who actually cares about their Public Folder should be caught unawares.