I know the forty-one words of the "Hail Mary" by heart. I learned to pray it as a child. And I'm old enough to still use the archaic pronouns of "thee," "thou," and "thy" when I recite it.
The Catechism of the Catholic Church has a beautiful line-by-line teaching on the "Hail Mary" that you can find in CCC 2676-2677. I invite you to read it at your leisure. But for now, let's turn to the prayer itself.
The first part of the "Hail Mary" is biblically based. As the prayer opens, we repeat the words of God, speaking through the angel Gabriel to Mary, to announce God's delight and favor in this chosen woman. (See Lk. 1:28.)
full of grace,
the Lord is with you."
These are words of God rejoicing over Mary at the Annunciation.
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. (Catechism of the Catholic Church, par 2676)
It continues, saying that Mary is full of grace—"filled [with] the presence of him who is the source of grace." This is an acknowledgement of Mary's Immaculate Conception. (See CCC 490-491.)
"Blessed are you,
and blessed is the fruit
of your womb,
These are the Spirit-inspired words of Elizabeth to Mary at the Visitation. (See Lk. 1:42.) Countless others through the ages have called Mary "blessed." Her example of faith is a beacon to us. Through her, we are blessed.
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." (Catechism of the Catholic Church, par. 2767)
The "Hail Mary" reaches its zenith in the words: "Blessed is the fruit of thy womb, Jesus." For Jesus is at the heart of Christian prayer.
Mother of God"
We find in these words the witness and declaration of the Church calling Mary "Mother of God." This is traceable to the scriptures and the early Christian Church.
Called in the Gospels "the mother of Jesus", Mary is acclaimed by Elizabeth, at the prompting of the Spirit and even before the birth of her son, as "the mother of my Lord". In fact, the One whom she conceived as man by the Holy Spirit, who truly became her Son according to the flesh, was none other than the Father's eternal Son, the second person of the Holy Trinity. Hence the Church confesses that Mary is truly "Mother of God" (Theotokos). (Catechism of the Catholic Church, par. 495)
"pray for us sinners now
and at the hour of death.
This last petition, echoing Mary's prayer at the Cross, declares the Church's confidence in Mary's holy intercession, help, and protection. We ask her to do the same for us.
This motherhood of Mary in the order of grace continues uninterruptedly from the consent which she loyally gave at the Annunciation and which she sustained without wavering beneath the cross, until the eternal fulfillment of all the elect. Taken up to heaven she did not lay aside this saving office but by her manifold intercession continues to bring us the gifts of eternal salvation. . . Therefore the Blessed Virgin is invoked in the Church under the titles of Advocate, Helper, Benefactress, and Mediatrix. (Catechism of the Catholic Church, par. 969)
The "Hail Mary" is true Christian prayer. We rejoice with God in what he has done in and through Mary to give us Jesus, and we invoke her help that we may give our own "yes" to God in our daily life—and at the hour of our death.
Mary's consent—her fiat, her "yes" to God, the perfect, loving response to the God's holy will—began with that glorious angelic encounter and holy overshadowing, and continued through her life, including her embrace of suffering at the hour of Jesus' death on the Cross. The last gift Jesus makes to the world before he dies is his mother. He gives her not only to the apostle John, but to the whole world, as mother.
Mary gave her consent in faith at the Annunciation and maintained it without hesitation at the foot of the Cross. Ever since, her motherhood has extended to the brothers and sisters of her Son who still journey on earth surrounded by dangers and difficulties. Jesus, the only mediator, is the way of our prayer; Mary, his mother and ours, is wholly transparent to him: she "shows the way" . . . and is herself "the Sign" of the way . . . (Catechism of the Catholic Church, par. 2674)