If you love youtube background music or any other audio then Cydia can help you grasp the audio out of the video with the help of an app. The video once converted to MP3 can played back on the iPhone or even shared with friends via email.
The app is called YouTubeToMp3 and now with updated version allows user to feed in the url of the video to be converted to Mp3. The app also supports multitasking enabling you to listen music while the app is busy converting the video to audio in the background.
YouTubeToMp3 is a free Cydia app available via BigBoss repo.