The Priority Inbox is a beta feature of Gmail. When enabled, Gmail attempts to prioritize important emails and show those messages at the top of your inbox. First you'll see all unread high priority messages, then you'll see messages with stars, and then you'll see everything else.
Just as with spam filters, the Priotity Inbox can be trained and improve over time as you indicate which items should be high priority. You can also specify that some messages are always high priority by using a Gmail filter.
Turn Priority Inbox on through your Gmail Settings menu on the Web.