Per the update section on the Google Play Store:
This update includes Listen Now – an all-new home for Apple Music, an all-new search experience, an enhanced playback experience featuring Autoplay, Crossfade, sharing to Instagram, Facebook and Snapchat Stories, and improved app performance.
In addition to a redesign, the menu has been updated as well. The “For You” tab has been updated to “Listen Now,” and search has been added to the menu.
With the update comes a redesign of the app, as originally outlined by Android Police, expanding out to five primary sections in the menu bar. Specifically, “For You” has been replaced with a similar, yet different “Listen Now” view, and the app’s search features have moved from an upper search bar down to the menu bar.
The Now Playing view has also been redesigned, displaying a dynamic background that will change color to match the album that is currently playing.
The Now Playing view has also been given a redesign, with a dynamic background that adjusts its colors to match the current song’s album cover. Open up the queue list to see another new feature of Apple Music 3.4, a new infinity-shaped icon on the right-hand side of “Playing Next.” With a tap of this button, autoplay will be enabled and show a preview of what automatically added songs will play next.
One of the most requested features for Apple Music was to allow sharing to popular social platforms like Instagram Stories, and the latest update adds that as well.
From any Apple Music song, album, or playlist, whether in Search or in your Now Playing queue, you’ll have the option to “Share” that bit of music, including direct to Instagram, Facebook, or Snapchat as a tappable sticker in your story. Selecting a different app simply shares a link to your selected album or track.