Below is a screenshot that Zain Memon managed to grab before it went away. Tabs like Recent, Replies, and Everyone have been moved to the right-hand column.
Overall, nothing too major. Corvida from SheGeeks points out some of the most obvious changes:
Tabs are now to the right of the screen
You can see the number of direct messages you have (not sure if that was there before)
Time stamps and “from” stamp are in italics
Latest tweet has been pushed under the “message box
Reply and Favorite shortcuts now appear as you hover over a message
If someone sent a message via text, the txt link takes you to the Official Twitter Commands page
The previous update also does the same for Twhirl, Twitterrific, and Twittelator. Meaning it takes you to their respective homepages
The search box was also moved (Thanks Orli!)
One thing conspicuously not included in the new design: advertisements, like the ones you’ll see on Twitter Japan.
Update: And another from the comments: