Here is a picture:
What does starring news items do?
(1) It lets Google know that you're interested in that subject.
(2) When there are significant updates, Google will alert you by putting the headline in bold so you can get more information.
(3) You can also follow your 20 most recent starred stories in the "Starred" section of Google News.
It also confuses some people. A Google News Help thread had one person ask:
Why are there pale blue stars in front of main stories?
Nothing is wrong: I'm just puzzled.
Forum discussion at Google News Help.