You'll first want to toggle "Play sounds outside the app" to OFF. To disable this, tap the sound icon in the top right corner of the home screen, and you'll see that option listed at the bottom of the Sounds menu.
Once that's disabled, start a meditation or story and turn your screen off, and the app will run until the session ends. If you'd like to just listen to background sounds, simply use the "Timed Meditation" option - set the timer to your preferred length, then turn your screen off. The background sounds will continue to play until the timer ends.