It is not applicable worldwide yet, but it will be in the next few weeks according Facebook.
To start using the feature once it's applied, simply point your eyes at Music Note on your online friends on the chat sidebar list.
And then hover your friend's name that is listening music. Then a small popup window will appear showing the song's name he or she is listening to, plus a button called: Listen With (your friend's name).
I believe this picture explains everything about Listen With feature.
This feature is not limited to one-on-one listening music ability, it can also bring your friends to your created group chat and invite them all to listen the music with you or your friend as DJ. And discover the music your friends like and love. Who knows they could be your favorite musics too.
Listen With feature is an expanded result of partnership between Facebook and music service Spotify, their partnership is growing into serving their users with ability to share Music to each other.