One of the alleged selling points for Microsoft's Bing search engine is more relevant results, so adding in recent posts from Twitter is an obvious thing to do.
Rather than aiming for full-blown Twitter indexing -- something Twitter itself has taken a while to get working -- Bing is indexing the results of "prominent" Twitterers, and only returning results if you include the word Twitter or an @ symbol in your query. If you're already interested enough in someone to search for their name that way, I'm not entirely sure seeing their most recent posts is that helpful (and their Twitter page should ideally be the top result anyway), but it's always good to have another option given how unreliable Twitter's own people search can be.
Based on the post announcing the feature, it looks like most of the selected Twitterers are US-centric, which has been the general approach with Bing all along. The feature is also being rolled out gradually; I couldn't see it on the bing.com.au site when I tested it (hence the borrowed screenshot); tell us in the comments if you find it working down under.
If (like most of us) you're still favouring Google over Bing, you can add real-time Twitter searches to Google results with a script.
Bringing a Bit of Twitter to Bing [Bing Community]