Origin unclear. Attributed to noted Edo-period botanist and scholar of Chinese medicine Ono Ranzan (see Wikipedia:ja:小野蘭山) in the late 1700s. May be from Sinitic 馬鈴薯, or may be a Japanese coinage later borrowed into Chinese.
According to one theory, this word is a compound of 馬 (ba, “horse”) + 鈴 (rei, “bell”) + 薯 (sho, “potato”), from the way the potato looks a bit like the bells used in the tack for stage horses. In another theory, 馬鈴 (barei) is an example of ateji for Malay, since potatoes were introduced to Japan via the Dutch East Indies.
馬鈴薯 (hiragana ばれいしょ, romaji bareisho)
- potato (Solanum tuberosum)
See also 
馬鈴薯 (traditional, Pinyin mǎlíngshǔ, simplified 马铃薯)
- 洋山芋 (yángshānyú) (regional)
- 土豆 (tǔdòu) (not in Taiwan)