1560s, "sweet potato," from Spanish patata, from a Carib language of Haiti batata "sweet potato." Sweet potatoes were first to be introduced to Europe; they were in cultivation in Spain by mid-16c. and in Virginia by 1648. Early 16c. Portuguese traders carried the crop to all their shipping ports and the sweet potato was quickly adopted from Africa to India and Java.
"This was the original application of the name, and it is in this sense that the word is generally to be understood when used by English writers down to the middle of the seventeenth century" [Century Dictionary].
The name later (1590s) was extended (based on general likeness, both being esculent tubers) to the common white potato, native to Peru, which was at first (mistakenly) called Virginia potato, or, because at first it was of minor importance compared to the sweet potato, bastard potato. Spanish invaders in Peru began to use white potatoes as cheap food for sailors 1530s.
The first potato from South America reached Pope Paul III in 1540; it was grown in France at first as an ornamental plant. According to popular tradition, it was introduced to Ireland 1565 by John Hawkins. It was brought to England from Colombia by Sir Thomas Herriot, 1586.
German Kartoffel (17c.) is a dissimilation from tartoffel, ultimately from Italian tartufolo (Vulgar Latin *territuberem), originally "truffle." Frederick II forced its cultivation on Prussian peasants in 1743. The French is pomme de terre, literally "earth-apple;" a Swedish dialectal word for "potato" is jordpäron, literally "earth-pear."
Colloquial pronunciation tater is attested in print from 1759. Potato salad is by 1842 as a typical German dish; by 1844 in English cookery books. For Potato chip see chip (n.1); for the British alternative potato crisp see crisp (adj.). Slang potato trap "mouth" is attested from 1785. The Potato Famine in Ireland from 1845 to 1849 was so called by 1851, mostly outside Ireland; in it it is typically the Great Famine, Great Hunger, or Great Starvation.
To drop (something) like a hot potato is from 1824. Children's counting-out rhyme that begins one potato, two potato is recorded by 1885 in Canada.