Mount Carmel is the place in the First Book of Kings where Elijah went to battle the pagan prophets of Baal and Astarte. The God of Israel demonstrated through Elijah the uselessness of pagan worship and the effectiveness of prayer to the true God. It represents the triumph of genuine faith over idolatry. As a result Elijah exhorted the people to reaffirm their faith in the true God. Mount Carmel therefore symbolizes the power of genuine prayer and a call to re-commitment to one’s faith.
The following is taken from the Catholic Encyclopedia: “This feast was instituted by the Carmelites between 1376 and 1386 under the title "Commemoratio B. Marif Virg. duplex" to celebrate the victory of their order over its enemies on obtaining the approbation of its name and constitution from Honorius III on 30 Jan., 1226 (see Colvenerius, "Kal. Mar.", 30 Jan. "Summa Aurea", III, 737). The feast was assigned to 16 July, because on that date in 1251, according to Carmelite traditions, the scapular was given by the Blessed Virgin to St. Simon Stock; it was first approved by Sixtus V in 1587. After Cardinal Bellarmine had examined the Carmelite traditions in 1609, it was declared the patronal feast of the order, and is now celebrated in the Carmelite calendar as a major double of the first class with a vigil and a privileged octave (like the octave of Epiphany, admitting only a double of the first class) under the title "Commemoratio solemnis B.V.M. de Monte Carmelo". By a privilege given by Clement X in 1672, some Carmelite monasteries keep the feast on the Sunday after 16 July, or on some other Sunday in July. In the seventeenth century the feast was adopted by several dioceses in the south of Italy, although its celebration, outside of Carmelite churches, was prohibited in 1628 by a decree contra abusus. On 21 Nov., 1674, however, it was first granted by Clement X to Spain and its colonies, in 1675 to Austria, in 1679 to Portugal and its colonies, and in 1725 to the Papal States of the Church, on 24 Sept., 1726, it was extended to the entire Latin Church by Benedict XIII. The lessons contain the legend of the scapular; the promise of the Sabbatine privilege was inserted into the lessons by Paul V about 1614. The Greeks of southern Italy and the Catholic Chaldeans have adopted this feast of the "Vestment of the Blessed Virgin Mary". The object of the feast is the special predilection of Mary for those who profess themselves her servants by wearing her scapular (see CARMELITES).”