Twitter is testing a search box on the root URL of its site, meaning on the home page and user pages. Currently, search resides on a subdomain, http://search.twitter.com. There is a "Find People" search on the root, but searching tweets is on the root.
The test will include a search box in the navigation in the top right of the page. Only a small subset of users will see the search box during the test.
Twitter has had a hesitant approach to search. While this may seem surprising on the surface, it has probably been necessary in the progress of the social network. As the popularity of Twitter grew, many of the users became accustomed to downtime, symbolized by the infamous picture of a whale being lifted by tiny birds.
As Twitter resolved the majority of their downtime issues, search became a possibility again. Twitter acquired Summize, which was a third-party search developed via the Twitter API. That's when search was placed on the subdomain.
It's good to see that Twitter is finding itself in the place to test search on the root domain. My gut tells me they'll find the search box very popular and roll it out to all users soon enough.