Cay·man Islands (kā'mən) A British-administered island group in the Caribbean Sea northwest of Jamaica, including Grand Cayman, Little Cayman, and Cayman Brac. The islands were discovered by Columbus in 1503. Georgetown, on Grand Cayman, is the capital. Population: 46,600. Cay·man'i·an (kā-mān'ē-ən) adj. & n.