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"Jewel Voice" is most likely an overly-literal translation of 玉音放送. A better translation might be "(The) Emperor's Voice".
The 玉 character means "jade", which can also be translated as "jewel". But jade has special significance in Japanese culture, often associated with royalty and divinity. In ancient Chinese history, which had a big influence on Japanese culture, many divine rituals involved jade; the prime deity of Daoism is the Jade Emperor.
This usage carried over into Japan, where the voice of the Emperor can also be called 鹤音 or "Crane's Voice" - the crane also has special significance in Japanese culture.
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According to Wikipedia's internal page on citogenesis (see no. 7), the specific origin of the mistranslation in congusbongus's answer is from a Wikipedia edit in 2006. From there, use of the term skyrocketed and created a situation were that translation was kept as it was now apparently supported by reliable sources (citogenesis). This was caught in September 2021 and fixed.