URL Droplet is a simple web app that allows you to paste in the download link for a file and have it download straight to your Dropbox, so you can deal with later. Using the web app, a user could start a large download while out on their mobile phone, on a company computer at work, or just sitting at an internet cafe.
The downloaded file is saved in the main Dropbox directory — if it were saved to public, anybody could see what you've been getting. Because of this, URL Droplet needs access to Dropbox, so you should be comfortable granting permissions to third-party apps. Thanks for the tip, Jeremy.