There are actually two different badges that Google is giving to developers of Chrome extensions. The first is the featured badge. That badge seems to be reserved for developers who adhere to all best practice guidelines including privacy, user experience, and clarity of listing page. The second badge is the established publisher badge. That badge is for developers who have gone through Google's identity verification process.
It appears that the purpose of these new badges is to make it easier to identify the more or less trustworthy Chrome extensions. That said, the cynic in me now wonders why Google hasn't required identity verification for developers all along.