Peer-to-Peer file sharing is to synchronize your files between computers. When you install a Sync app at a directory on your computer, you share those files with any other computer that you give a secret pass code to. The data only lives on your computer and the computers you share it with (or mobile phones). It's never uploaded to a third party server like other file syncing programs. Since you data are never uploaded to a server, your storage capacity is only limited to your own hard drive, and no one else has access to your files.
The downside to Sync is that your home computer must be on at all times if you want synchronize files. This is great as a security measure because your private data is never on a server, but it does make accessing files a bit of a pain.
Likewise, sharing is a bit more complicated with Sync than it is with most file syncing services. If you want to share files with other people, they'll need Sync software installed as well as a secret code you generate and send to them.
Sync isn't quite as easy to use as something like Dropbox for everyday file backups, but it's still a solid option for file syncing. Most importantly, Sync is one of the most secure ways to sync files because your data never goes to a server. That means that nobody can peek in on your private files.
Besides the security, Sync is also great because it isn't limited by space—you don't need to worry about cloud storage limits, since the only limits are your own hard drives (which are likely much bigger than Dropbox's 2GB of space, or even Box's 50GB of space).
In addition, it's also one of the best ways to share a massive amount of files with someone. Since Sync is free it's easy to share project files with coworkers, large videos with friends, or any other massive folder you need to share. As long as they also have Sync, of course.
For example, if you're working on a movie with a partner, you probably have a folder with a couple hundred GB of video in it. With Dropbox, this would be expensive to store and share with your partner, but Sync keeps your computers in sync with each for free. Any time you need to send a massive file to someone, Sync will prove helpful.