When you play a track, bring the full album art up large on the screen. You'll see a little hint of a black tab peeking out from behind the art that says "Behind the Lyrics" -- slide the album cover down with your finger, and boom.
For now, the feature is only accessible on the latest version of the mobile app -- and it's only on certain tracks (the ones that have annotated lyrics on Genius). So if you don't see the black tab behind the cover art, you're out of luck, but it's still fun to discover them hiding behind your favorite tracks.
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