St. Pius V (April 30) established this feast in 1573. The purpose was to thank God for the victory of Christians over the Turks at Lepanto—a victory attributed to the praying of the rosary. Clement XI extended the feast to the universal Church in 1716. (taken from American Catholic.org)
“The rosary, though clearly Marian in character, is at heart a Christ-centered prayer. It has all the depth of the gospel messge in its entirety. It is an echo of the prayer of Mary, her perennial Magnificat for the work of the redemptive Incarnation which began in her virginal womb.... It can be said that the rosary is, in some sense, a prayer-commentary on the final chapter of the Vatican II Constitution Lumen Gentium, a chapter that discusses the wondrous presence of the Mother of God in the mystery of Christ and the Church" (Pope John Paul II, apostolic letter The Rosary of the Virgin Mary).