Overall, this looks like a better implementation of Twitter Search than the original idea, which had only been rolled out to a small number of users, and which hid the search feature away in a small box at the top of the page. Twitter says that the earlier version of its new homepage was not well received by its testers.
Clearly, adding search - and adding persistent searches in the sidebar especially - is a way for Twitter to get users to come back to their homepages regularly. For Twitter's most active users, the current homepage simply doesn't offer enough of the features they are used to from their desktop clients. However, if Twitter wants to monetize its service through advertising on its site (and the small ads that started to appear on the site in the last few weeks make us believe that this is the way Twitter is planning to go), it will have to give users a reason to come back to its site.
Twitter has also clearly recognized the real value of its service, besides offering a way for users to communicate, is in its real-time search.
As of now, Twitter is only testing this new homepage with a select number of users. The company will test the current iteration of the homepage with these users and then roll these features out to all users "as soon as possible" - assuming, of course, that the Twitter team doesn't decide to go back to the drawing board again.