If a story pops up in Google News that you'd like to keep track of, you can now add a familiar "star" to it. That allows you to track multiple stories from a "Starred" menu, and get updates on new developments.
When a story is starred, updates to it will cause bold-face headlines to appear and, presumably, draw your eyes to them. You can also check in manually on your stories by visiting "Starred", but Google has, for some reason, limited your starring to 20 recent items. Perhaps it's a matter of how much they can put on a page, or a person can realistically follow, but it seems an odd, artificial limit for such a vast service.
Starring stories in Google News [Google News Blog]