If you wish to listen to your playlists offline, you can do so by downloading it to your Android device.
1. Select your playlist.
2. At the top of the screen is a switch, which once turned on will automatically start downloading the tracks in the playlist to your Android device.
3. Once downloaded, you will see a green dot next to the playlist in the playlist view, and next to each track in the playlist itself.
4. If you want to check the progress of the download, go to Settings > Download Queue.