At the side of every diary is a box that says "Vote story to Front Page". If enough people vote "Yes" in this box, the diary will be displayed on the front page as well as the diary page.
However as some authors might not want their diary on the front page, the final decision is up to them. When enough people have voted a diary to the front page, the author is sent an email informing them of this. To actually put the story on the front page they must then vote "Yes" in that box as well.