After the song became a hit in 2007, the Japanese virtual idol software Hatsune Miku, powered by the voice synthesis software VOCALOID2 (and later released in a version called Mirror Voice), took it to cultures outside of Japan and made it a huge hit.
The song was nicknamed the "onion flinging song" in Chinese after Hatsune Miku's "onion flinging" imitation of Loituma Girl. The Japanese lyrics of "Shake Onion Song" are just a transliteration of the original lyrics, and are practically meaningless. (Bolded text quoted from the lyrics of the song)
The classic "onion flinging" move has since been imitated by most people, resulting in the "onion flinging dance".
The details can be found in the lyrics of the Onion Flip Song.