It's in beta now, it's got a name, BitTorrent is calling it SoShare and you can sign up to use it straight away.
SoShare uses BitTorrent technology to make it possible to share huge files with friends and colleagues from your computer.
In essence, it's more similar to Dropbox or perhaps Mega than to the BitTorrent network, you select a file you want to share, it gets uploaded to the cloud and it becomes available to those you share it with even if you're offline.
You'll need a browser plugin to make all of this work, another tool BitTorrent has been working on lately.
There are plenty of cloud storage and file sharing tools and services around. What makes SoShare unique is the peer-to-peer technology which should allow it to keep costs minimal which, in turn should mean very small prices for users. It's completely free during the beta.