One of the big advantages of using Dropbox is that it lets you easily recover files that you may have accidentally deleted from your computer’s hard drive. Should you wish to restore a file that is no longer available on your computer, just go to the “Deleted files” section of the Dropbox website and select the file that you want to recover.
When you delete a file from a local folder, Dropbox will not remove that file from their own servers, instead they will simply move it to another folder from where you may restore it later. This is much like the Recycle bin of Windows – deleting a file will only move it to the Recycle bin and you have to manually empty* the bin to permanently remove that file.
Coming back to Dropbox, if you would like to get rid of a file permanently so that it also gets deleted from Dropbox servers, first delete that file from your computer.
Next, log in to Dropbox website, choose the “Show Deleted Files” option, select the file that you just deleted and then click More –> Permanently Delete to trash it forever. The screencast above explains the steps in greater details.
[*] In fact, it is a bit complex at the OS level. You should securely delete your Windows files else they can be recovered even after you have emptied the Recycle bin.