Some of the most notable improvements include an expanded Friends List to let players keep closer tabs on what their contacts are playing, a new in-game overlay design with more context sensitive information, redesigned Steam store, and several other UI changes that should improve the discoverability of features and better expose all the information related to games in your library. They've also swapped out the Internet Explorer web browser rendering engine with the faster and more stable WebKit.
A full rundown of the new features can be found at the Steam website. To grab the beta you need to have the current Steam client installed, go to File>Settings, click "change" under Beta participation, and then choose UI Update. The beta should download automatically and will be available after restarting the client.