It stores files and allows you to download them.

Is that all? No. All the files are encrypted **by the browser**! It means that your files **never** leave your computer unencrypted.
The administrator of the Lufi instance you use will not be able to see what is in your file, neither will your network administrator, or your ISP.

The encryption key part of the URL is a anchor (Cf. [Fragment Identifier](https://en.wikipedia.org/wiki/Fragment_identifier)), that means this part is only processed client-side and does not reach the server. :-)