To startle people with a cry
This is used when a person generally does not appear to do anything impressive/be out of the ordinary, but then astounds others by accomplishing a great feat
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这次技术大比武中，他一鸣惊人，夺得了第一名 | Zhè cì jìshù dà bǐwǔ zhōng, tā yīmíngjīngrén, duó dé le dì yī míng
In the martial arts competition, he shocked everyone by getting first place
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老王平时默默无闻，这次却写出了震动学术界的论文，真是一鸣惊人 | Lǎo wáng píngshí mòmòwúwén, zhè cì què xiě chū le zhèndòng xuéshù jiè dì lùnwén, zhēn shi yīmíngjīngrén
Old Wang was a nobody, so him writing a paper that shook the academic circles was really astounding
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There is another version of this story that is almost identical, except for the fact it takes place in the ancient state of Qi (齐国, Qí Guó)
《韩非子》(Hán Fēi Zǐ), a book of philosophy authored by 韩非 (Hán Fēi) during the Warring States Period (475 - 220 BC)
There once was a king of 楚 (Chǔ) who for three years focused only on drink and pleasure. During this time, corruption ran rampant and state of the country suffered drastically. Loyal officials tried to speak to the king, but their attempts stopped when he threatened to execute anyone who opposed him or suggested that he start acting responsibly.
Finally, though, one brave official approached the king and said that he had a riddle that he wanted him to solve. The monarch was intrigued, and so the official asked him whether "he knew what kind of bird had neither flown nor sung for three years."
The king immediately knew that the official was not actually talking about a bird, and he replied, "Once that bird flies, it will fly high in the sky. Once it makes a sound, it will startle the world (一鸣惊人)." After that, the king started governing seriously, and he eventually led the kingdom into a position of notable power during the Spring and Autumn Period (770 - 476 BC).