Cultivated potatoes all belong to one botanical species, Solanum tuberosum, but this includes hundreds, if not thousands, of different varieties. The 200 wild potato species originated in the South American Andes inhabiting a range that extends from high cold mountains and plateaus into warmer valleys and subtropical forests and drier semi-arid regions and coastal valleys.
According to 'The Cambridge World History Of Food' (edited by Kenneth F. Kiple and Kriemhild Coneè Ornelas, and published in two volumes by Cambridge University Press in 2000) it was Spanish explorers who first encountered the potato in Peru, Bolivia, Colombia, and Ecuador in the 16th-century. They compared the unfamiliar tuber to truffles, and adopted the Quechua name 'papa'.
The first specimens probably reached Spain around AD 1570. Sailors returning from the Andes to Spain with silver presumably carried maize and potatoes for their own food on the trip. It is speculated, therefore, that leftover tubers (and maize) were carried ashore and planted. From there, the potato spread via herbalists and farmers to Italy, the Low Countries and England. There was likely a second introduction of the potato to England sometime in the following twenty years. On Sir Francis Drake's round-the-world voyage (1577 to 1580), for example, his first encounter with potatoes was recorded in 1578 off the Chilean coast. Despite British folklore crediting Drake with the introduction of the potato to Britain, this could not have been the case as it is highly unlikely that the tubers would have survived a further two years at sea.
Further reading:
1. Writing for BBC Travel in March 2020, Diego Arguedas Ortiz provides a more in-depth history on 'How the humble potato changed the world'.
2. Alternatively, Gerard Paul (April 2021) has taken a comprehensive look at the history of the potato: from their origin in modern-day Peru, to their cultivation and worldwide spread, to their contribution to warfare and global population growth.