In a nutshell, Mozy is a backup application which backs up your files to Mozy's servers. As you might guess, this requires the use of the Internet, and perhaps just a little magic. The backups are encrypted, so you don't have to worry about someone peeking at your files or taking some of your MP3s for their own collection. Mozy also ships with 'Backup sets,' which are predefine file locations and the like to make backing up easier. For example, the iTunes Library Backup Set will target your (shockingly) iTunes library, while the Desktop Backup Set makes sure all the files on your Desktop are backed up. You can even create Backup sets of your own, which I did to backup only those items that I bought via the iTunes Store.
The application itself is free because Mozy makes their money charging for the storage your back ups use. A free account will get you 2 gigs of back up space, while $4.95 per month will get you unlimited space (and if you pay for a year or two in advance you get a few months for free).
I signed up for a free account and took Mozy for a spin. Overall, the application is just what you want from a backup app: unobtrusive and easy to use. The downside to Mozy, and this is true of any system that backs up over the network, is speed (I know that the topic of upload/download speeds is fertile ground, but that discussion is outside the scope of this post). I backed up 1.4 gigs using Mozy and it took 4.5 hours.
Check out this gallery for lots of screenshots of Mozy, as well as a look at how one restores files from back up.