Update - 19 September 2012
Twitter has updated its layout again, go here to find out how to get it - How To Get The New Twitter Layout
Well this was unexpected. So many tech sites and services are have been getting overhauls recently, looks like Twitter is next.
The new Twitter has been redesigned completely. The bar at the top has been changed around a little, adding a home, connect and discover button. The Twitter logo now comes in the centre and the search, profile and tweet button are on the right. Everything has its own section now on top of rounded-off white panes. The homepage has been re-organised completely with the latest tweets now on the right side. On the left are sections to your profile and a quick tweet box, as well as, "Who to follow" and trending topics boxes.
When you click on a tweet, it now expands right in the timeline, making a more unified experience. You can look at images and watch videos right in the timeline without ever having to leave Twitter.
Twitter are making a great move here and making the web version of their service a lot more engaging. I'm guessing this is so that more people use the web version which means more people get fed advertisements.
How To Get The New Version of Twitter
To get the new version of Twitter you have to download either the Android or iOS app, that's all you have to do. Then it should appear. I had to wait around an hour or two for it to activate the new version, it does it automatically.
I don't know why Twitter didn't make the activation method easier. But it looks like they want more people to adopt their Android and iPhone apps.