Sync enables to have Firefox on several devices and to sync bookmarks, passwords, history, and other browser data between them.
There's nothing wrong with Mozilla, they're big champion of Free Software. But on the one hand, there's definitely something troubling with sending very private data such as browsing history over the internet. Fortunately, Sync encrypts locally before uploading data and I hope they’re up to the Free Software standards of crypto.
On the other hand, centralisation is often a problem (don't put all your eggs in the same basket!). First, it puts the burden of maintaining huge Sync servers on Mozilla whereas a lot of users could be running Sync themselves and thus do a favour to Mozilla. Second, Mozilla becomes a single point of failure in case something's wrong with Sync; and with all the crazy stuff NSA’s been doing lately avoiding single points of failure is good because it raises the costs of surveillance.
And really, it is so simple to set up, that you really wonder why you haven't done it before!
[I’m starting yet another folder on this blog/wiki where I'm going to post some of the ?configs for my home servers.]