If the Mac App Store finds an update available for a running app, it’ll prompt you to allow it to quit the app in order to apply the update. Once it’s finished (and you didn’t manually quit the app yourself), the app will relaunch. As long as it’s a fairly modern app that supports Resume, a feature that appeared in OS X Lion, the app will bring you and any open windows right back to where you left off.
After asking Twitter, relaunching an app after the Mac App Store updates it seems to be exclusive to Mountain Lion.

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