From the Less Wrong FAQ:

Posts are "promoted" to the front page by the editors on the basis of substantive new content, clear argument, good writing, popularity, and importance. The posts with karma totals in green disks instead of gray circles have been promoted.

I don't actually know. For all I know, articles become Promoted when Eliezer likes them enough to do background things in the blog. Maybe I should repost this in Discussion as well. I might worry that that would irritate people who see it twice, though.