Understanding the Hail Mary...
Catechism Reference 2676:
Hail Mary [or Rejoice, Mary]: the greeting of the angel Gabriel opens this prayer. It is God himself who, through his angel as intermediary, greets Mary. Our prayer dares to take up this greeting to Mary with the regard God had for the lowliness of his humble servant and to exult in the joy he finds in her.
Full of grace, the Lord is with thee: These two phrases of the angel's greeting shed light on one another. Mary is full of grace because the Lord is with her. The grace with which she is filled is the presence of him who is the source of all grace. "Rejoice . . . O Daughter of Jerusalem . . . the Lord your God is in your midst." Mary,
in whom the Lord himself has just made his dwelling, is the daughter of Zion in person, the ark of the covenant, the place where the glory of the Lord dwells. She is "the dwelling of God . . . with men." Full of grace, Mary is wholly given over to him who has come to dwell in her and whom she is about to give to the world.
Blessed art thou among women and blessed is the fruit of thy womb, Jesus. After the angel's greeting, we make Elizabeth's greeting our own. "Filled with the Holy Spirit," Elizabeth is the first in the long succession of generations who have called Mary "blessed." "Blessed is she who believed. . . . " Mary is "blessed among women" because she believed in the fulfillment of the Lord's word. Abraham. because of his faith, became a blessing for all the nations of the earth. Mary, because of her faith, became the mother of believers, through whom all nations of the earth receive him who is God's own blessing: Jesus, the "fruit of thy womb."