The Roman agricultural writer Palladius praised alfalfa as a forage crop, and he called it by the name "Medica" because it was a plant supposed to come from the Medes who lived in ancient Persia. It is from this Latin name that alfalfa gets its scientific genus name: Medicago. Alfalfa was introduced to Spain during the Umayyad conquest in the eighth century, hence the use of the Arabic name al-fisfsa, which became Spanish alfalfa. You can read more about Alfalfa in this Wikipedia article.
The image below shows an alfalfa field:
