The Onion Router often just called TOR is a multiple layer proxy software that promises full anonymity to all the users who use it. It is frequently used by journalists to communicate with their peers when sharing sensitive information. And now there is an open source software called OnionShare available that allows you to share files through the TOR network and as such gives you the shield of complete anonymity.
This software lets you securely and anonymously share files of any size. Unlike the TOR browser, OnionShare works by running a web server on your PC, making it accessible as a Tor onion service, and generating a random URL to access and download the files. In simple words, you host the files on your own PC and make them accessible through TOR network. If you close the OnionShare web server, then the files become unavailable. Anybody who wishes to download your files can download them using the Tor Browser.
The problem with this approach is that by running a web server on your PC, you are exposing yourself to many risks. Since TOR security has been breached before and perhaps it can be done again in the future, your real IP address can become visible. And if you are running a web server, then it becomes easy for a potential hacker to target your PC.
OnlineShare is only for a few people who are totally paranoid about the security of their network or computers. For everyone else, there are so many other ways to share the files. For example, if you want to temporarily share some files with someone, then you can use many well known and secure cloud sharing services like Box, Dropbox, Google Drive, OneDrive and many others. In all of these cloud storage providers, there are options to create sharing links only for individuals and this way you can share your sensitive data with anyone you wish. In case you are worried about uploading your files to cloud storage services, there are so many tools that encrypt cloud storage contents.
Verdict: OnlineShare helps you share files over the TOR network, but it is meant only for paranoid users. Since it runs a local web server on your PC, it can result in exposing your system or your files to other people in case of a TOR network breach.
You can find more information about OnlineShare at https://github.com/micahflee/onionshare/.