The seemingly only change in the update is the ability to change the name and description of a playlist, as well as to share your playlist with friends, straight from the device. Previously, these features were only available in the web interface of Google Play Music. To access these new features, just click on the Menu button and pick them from the overflow menu.
Play Music version 5.5.1509O should be heading your way right now, though you can check for yourself from the My Apps section of the Play Store. Or, if you’re new to it, check the Play Music app in the Play Store.