Previously, Twitter has used this space to display links to its own services and Twitter-related third-party tools and services, but now it's showing pure ads that take you to sites such as ABC News or NFL.com.
Interestingly enough -- as noted by Labnol -- Twitter does not use the "nofollow" tag or disclose the fact that these are ads at all, except by defining them under the CSS class "promo," which is visible only if you look at the HTML code.
Twitter has been experimenting with several different ad formats and possible revenue streams in the past year or so, adding ads to the individual user streams in November and letting select customers advertise through Promoted Tweets, Trends or Products. The text ads on the homepage probably aren't as important for Twitter as other ad formats, but the company is methodically trying every possible advertising avenue to figure out what works best.