I can't seem to find out the reason behind the naming of the audio Jewel Voice Broadcast.
I learned that this broadcast was the first instance of the Emperor directly communicating to masses. I can speculate that perhaps this had something to do with the naming. Or perhaps the voice of Emperor was called so in veneration. Or maybe it's just a transliteration of Gyokuon-hōsō (which still begs the question why it was compared with Jewels).