Somewhere on a Dropbox server is a file that you want. Normally the file's owner would have to share that file with you in order for it to appear in your Dropbox. But if you know the hash of file you can trick Dropbox into thinking you already have the file and are just adding it to your Dropbox. Apparently Dropbox notices they already have that file, and instead of you uploading it they just make it appear in your account. Then you can download it.
I wasn't impressed by the OP, but this is actually a really cool hack.