From the Catechism of the Catholic Church, Simplified
Mary and Jesus (487-488)
The Church's teaching about Mary illumines our faith about Christ. In preparing a body for Jesus (Heb 10:5) God wanted a creature's free cooperation. He chose Mary (a daughter of Israel and a virgin betrothed to Joseph) to be his Son's mother. A woman (Eve) had shared in the coming of death, so a woman should share in the coming of life (Second Vatican Council).
Holy Women (489)
Many holy women prepared for Mary. Eve received the promise of a posterity who will win the victory over the evil one. She is called "the mother of all the living" (Gen 3:15, 20). Sarah and Hannah conceived children in their old age. Among all women, Mary "stands out among the poor and the humble" and "the new plan of salvation is established in her" (Second Vatican Council).
Conceived without Sin (490-491)
Mary was enriched with gifts appropriate to her call. She was "full of grace" (Lk 1:28).
Over the centuries, the Church realized that this "full of grace" meant that Mary was redeemed from the first moment, her Immaculate Conception. Mary, "from the first moment of her conception by the merits of Jesus Christ, was preserved immune from all stain of original sin" (Pope Pius IX).
Redeemed by Christ's Merits (492-493)
By Christ's merits, Mary "is redeemed in a more exalted fashion" (Second Vatican Council). The Father blessed Mary "in Christ with every spiritual blessing" and chose her "in Christ before the foundation of the world, to be holy and blameless" (Eph 1:3-4).
The Eastern Church calls Mary "the All-Holy" and says that she is "free from any stain of sin... formed as a new creature." By God's grace, Mary remained free of personal sin throughout her life.
Total Gift of Self (494)
Mary responded with the obedience of faith. "Behold, I am the handmaid of the Lord, let it be done to me according to your Word" (Lk 1:28-38). She gave herself entirely to the person and work of her Son. Church writers call Mary "the Mother of the living." "Death came through Eve, but life through Mary (St. Jerome)."
Truly - The Mother of God (495)
She is seen as "the mother of Jesus." However, Elizabeth, moved by the Spirit, rightly calls Mary "the mother of my Lord" (Lk 1:43) because she conceived the second person of the Holy Trinity. The Church proclaimed that Mary is truly Mother of God, "Theotokos" (Council of Ephesus).
Conceiving Yet Remaining a Virgin (496-498)
The Church has always taught that Jesus was conceived "by the Holy Spirit without human seed" (Lateran Council). This virginal conception was the sign that Jesus was truly the Son of God. He is "truly of the race of David according to the flesh, Son of God according to the will and power of God, truly born of a virgin" (St. Ignatius of Antioch).
This virginal conception is beyond human understanding. Joseph had to be told, "that which is conceived in her is of the Holy Spirit" (Mt 1:20). Isaiah had prophesied: "Behold, a virgin shall conceive and bear a son" (7:14).
Faith in Jesus' virginal conception met with lively opposition from Jews, unbelievers, and pagans (St. Justin). This opposition shows that the virginal conception was not some adaptation of a first century belief. Mary's virginity, her giving birth to Jesus, and the Lord's death are three mysteries which were "accomplished in God's silence" (St. Ignatius).
Always a Virgin (499-501)
In giving birth, Mary's real and perpetual virginity was not diminished but was sanctified (Second Vatican Council).
Sometimes the Bible mentions brothers and sisters of Jesus. The Church has always seen these "brothers and sisters" as not being other children of Mary. In fact, Matthew speaks of "his brothers James, Joseph" who are actually the sons of "the other Mary" (13:55, 28:1).