It uses Twitter activity, including Tweets and engagement, to detect and surface the most popular tracks and emerging artists. It also brings artists' music-related Twitter activity front and center: go to their profiles to see which music artists they follow and listen to songs by those artists. And, of course, you can tweet songs right from the app.
The key point is Twitter isn't launching a music service, but a discovery engine. Actual music will initially be served from iTunes, Spotify or Rdio. Previews will by default come from iTunes while subscribers to Spotify and Rdio can log in to hear streams of full songs. For the launch, the service is available in the US, Canada, UK, Ireland, Australia, and New Zealand.
The way the system works is you can browse music using a #NowPlaying view. That will show songs that have been tweeted by the people you follow. Also, you can view charts of music and click on individual artists. That card will tell you about the artist and their top song. You can also search out music using Twitter.
The update is available in the latest version of the Twitter app.