What Jamaica means
Jamaica is a Mexican drink name of Spanish origin meaning "hibiscus, roselle". It comes from Spanish jamaica (roselle calyx), from the island name Jamaica, from Taíno Xaymaca (land of wood and water). It is pronounced hah-MY-kah, and it is most associated with the whole country.
The plant is African in origin, so the Spanish name records the Caribbean trade route rather than the source. How firmly the flower name attaches to the island is not certain; the island's own name is securely Taíno.
This is a site about what Mexican words mean, so there is no recipe here. For the name itself: Agua fresca, horchata, atole, tepache, pulque, mezcal. Most Mexican drink names are the name of the plant or grain they are made from, and the agave spirits are named for the towns and regions that make them.
