I think Biz explains the reasoning behind the re-design best in his blog post when he says:
Defining a “tweet” for the uninitiated and explaining how to create an account doesn’t resonate with everyone. “Why would I want to do that?” is a common reaction. However, demonstrating the power of Twitter as a discovery engine for what is happening right now through our Search and Trends often awakens a sense of wonder which inevitably leads to a much more compelling question, “How do I get involved?”
Personally, I love the simplicity, it’s the google simplicity approach, putting the search front and center is a very strong move. Has me wondering why they just got around to it. And the clear call to action “sign up now” next to it is great placement. Then the hashtag list thing at the bottom giving visitors a taste and quick links really drives the power of twitter search home.
Update: Gary Vaynerchuck on Twitter’s redesign: