More Chrome Web App features arrive in Chromium builds
Among the more recent additions is support for background apps, which have actually been part of the Chromium source code for a while now. Unlike the Chrome Apps you may have tried already (like those for Gmail, Docs, and Calendar), background apps can function continuously even though you don't have them open in a tab.
Recently, background app support was added to about:flags. In the current Chromium snapshots (and in the Chrome Dev Channel and Canary), enabling the feature now adds an additional option to your Under the Hood settings -- check the box to enable background apps and run them at startup. Google's choice of "system start" is a nod to Chrome OS, where background apps will likely be the equivalent of system tray apps on your current operating system.
... And don't get your hopes up about that learn more link. Currently, it points to a non-existent page, which isn't surprising considering the Web Store isn't open yet.