First, the history. The Rosary was given by the Blessed Virgin herself to St. Dominic in ARSH 1214. St. Dominic was having a terrible time combating heretics that were deeply embedded in the Church. (D’oh! Sound familiar??) Long story short, she appeared to St. Dominic and told him what the Holy Trinity wanted done. Her words were, “I want you to know that, in this kind of warfare, the battering ram has always been the Angelic Psalter which is the foundation stone of the New Testament. Therefore if you want to reach these hardened souls and win them over to God, preach my Psalter.”
The Angelic Salutation are the words of the angel Gabriel to Mary from Luke 1:28: ”Hail, full of grace, the Lord is with thee: blessed art thou among women.”
The rest of the prayer then quotes the words of Mary’s cousin Elizabeth, the mother of John the Baptist, upon Mary’s arrival at her home to be with her through her miraculous post-menopausal pregnancy in Luke 1:42: ”Blessed art thou among women, and blessed is the fruit of thy womb.”
The rest of the prayer asks Our Blessed Lord’s mother to pray for us to her Son now, and especially at the hour of our death.