Mount Carmel is a ridge above the bay of Haifa, and its religious history begins long before any Christian order. It is where the first book of Kings sets the contest between Elijah and the prophets of Baal, and where Elijah's servant, sent to look out to sea seven times, at last reports a little cloud rising out of the water the size of a man's hand, which breaks a three year drought. Carmelite tradition reads that cloud as a figure of Mary, and the reading ties the order's two founding attachments together in a single verse.
Latin hermits were living on the mountain by about 1200 and received a rule from Albert, patriarch of Jerusalem. As the crusader position collapsed they migrated to Europe, reconstituted themselves as a mendicant order, and carried the mountain with them in their title: the Brothers of the Blessed Virgin Mary of Mount Carmel.
The feast follows the order rather than the other way round. Carmelites kept a commemoration of their patroness from the fourteenth century; it spread with them; and in 1726 Benedict XIII extended it to the whole Latin church, on 16 July. The calendar reform of 1969 reduced it to an optional memorial in the general calendar, which changed its rank without making the slightest difference to how it is kept in the places that keep it.