This according to Twitter Developer Advocate Taylor Singletary, who has just updated the developer Google Group announcing the yet-to-be-released product. Singletary says, "This is a beta project, but an important first step to surface the most popular tweets for users searching Twitter."
The announcement is geared toward developers to prepare them for changes in the search API. The implication, however, is that the appearance of Twitter Search will also be altered to highlight popular tweets. Ultimately, it appears that the revamped search experience will be available on both Twitter.com and third-party applications and clients that move to support it.
While there's no word on how "popular" is defined by Twitter, we can assume that the popular tweets will be identified by attributes such as quantity of retweets or potentially tweets coming from a user with a high level of followers and engagement.