Chrome OS is a Linux OS. It is essentially just the Chrome browser, with some local storage for limited file storage and off-line enabled HTML5 apps.
The advantage is without the bloat of the rest of a traditional OS, Chrome OS runs very well on low-powered hardware and can boot in under 10 seconds. The low-powered hardware also means lengthy battery life.
The disadvantage is that you can't (easily) run anything that isn't available in the browser or Chrome web store. Also, without a persistent internet connection, functionality is extremely limited (though offline Docs work now).
Personally, Chrome OS works very well for me. I ran it on an Acer Aspire One for over a year, squeezing new life from the borderline obsolete first generation Intel Atom. Now I have a Samsung Series 5 550 and it is easily the smoothest and nicest laptop I've ever owned. That said, it's certainly not for everyone.
is a YouTube video by The Verge from April, when Chrome OS received a major update to the current Aura UI. If you're interested, a guy named Hexxeh compiles Chromium OS (the open source version) nightly and makes the builds
available to anyone to download. If you have compatible hardware (usually netbooks work best), you can run it off a USB key to try it out.