Your operating system can run processes in the background -- things like realtime antivirus protection and streaming movies and music around your home -- and so can Google Chrome. Background apps have existed in Chrome and Chromium for some time, but now that the Chrome Web Store is open and its apps are available for installation, Google has posted a blog about why backgrounding is cool.
It's really all about Chrome being your "OS" even if you're using a Windows or Mac computer. With the ability to run Web apps in the background and Native Client support headed to the beta and stable channels in relatively short order, Chrome Web Apps will soon be capable of doing many of the same things your traditional desktop apps can do.
Google's post talks about using backgrounding to issue notifications (as apps like TweetDeck and exfm do) or to prefetch data. There's really no end to the possibilities, and we're exited to see what the next generation of Chrome Web Apps can really do.