Mary is the mother of God, and a great example for each one of us. She accepted the will of God for her life, although this acceptance entailed a radical upheaval in her life and the abandonment of a normal existence for a life of great joy and sorrow, and of uncertainty. As the mother of Jesus, she has a special relationship to Him and is the greatest intercessor on our behalf with Jesus, for He will not refuse His mother any request she makes.
Catholics don't worship Mary
Mary has a special place in the Catholic Church, and is very highly revered. Other Christian denominations don't necessarily agree with the honor which is given to Mary, perhaps because some of them think erroneously that Catholics adore Mary. No one is worthy of adoration except God, but we do honor Mary as a celebration of her life of perfect virtue and as a role model for each one of us, to remind us how we should live our lives in accordance with God's will.
Mary in the Bible, especially prefigured/OT
Mary is mentioned on numerous occasions in the New Testament, particularly in the gospels of Matthew, Luke and John. However, even in the Old Testament, there are prophecies and references to her, showing that she was a part of God's plan of salvation from the beginning. “I will put enmity between you and the woman, and between your seed and her seed; he shall bruise your head, and you shall bruise his heel.” - Genesis 3:15. At the very beginning, just after the fall of Adam and Eve, God promises that a woman and her son will be combatants of and defeat the devil. This promise was fulfilled in Mary. “Therefore the Lord Himself shall give you a sign: Behold, a virgin shall conceive and bear a son, and shall call his name Immanuel” - Isaiah 7:14. This prophecy by Isaiah also speaks of Mary and her mysterious conception while still a virgin by the power of the Holy Spirit.
Early Church Fathers Mary's role in salvation
The early Christian writers had a very high estimation of Mary and her role in salvation. They saw her as the new Eve, the one who brought about the savior and was instrumental in reversing the bad effects of Eve's selfish decision at the beginning of the world. They also speak of several doctrines which the Catholic Church holds about Mary.
[Jesus] became man by the Virgin so that the course which was taken by disobedience in the beginning through the agency of the serpent might be also the very course by which it would be put down. Eve, a virgin and undefiled, conceived the word of the serpent and bore disobedience and death. But the Virgin Mary received faith and joy when the angel Gabriel announced to her the glad tidings that the Spirit of the Lord would come upon her and the power of the Most High would overshadow her, for which reason the Holy One being born of her is the Son of God. And she replied ‘Be it done unto me according to your word’ (Luke 1:38). - Justin Martyr Dialogue with Trypho the Jews 100
Consequently, then, Mary the Virgin is found to be obedient, saying, ‘Behold, O Lord, your handmaid; be it done to me according to your word.’ Eve, however, was disobedient, and, when yet a virgin, she did not obey. Just as she, who was then still a virgin although she had Adam for a husband—for in paradise they were both naked but were not ashamed; for, having been created only a short time, they had no understanding of the procreation of children, and it was necessary that they first come to maturity before beginning to multiply—having become disobedient, was made the cause of death for herself and for the whole human race; so also Mary, betrothed to a man but nevertheless still a virgin, being obedient, was made the cause of salvation for herself and for the whole human race...Thus, the knot of Eve’s disobedience was loosed by the obedience of Mary. What the virgin Eve had bound in unbelief, the Virgin Mary loosed through faith. - Irenaeus Against Heresies 3:22:24
And again, lest I depart from my argumentation on the name of Adam: Why is Christ called Adam by the apostle [Paul], if as man he was not of that earthly origin? But even reason defends this conclusion, that God recovered his image and likeness by a procedure similar to that in which he had been robbed of it by the devil. It was while Eve was still a virgin that the word of the devil crept in to erect an edifice of death. Likewise through a virgin the Word of God was introduced to set up a structure of life. Thus what had been laid waste in ruin by this sex was by the same sex reestablished in salvation. Eve had believed the serpent; Mary believed Gabriel. That which the one destroyed by believing, the other, by believing, set straight. - Tertullian The Flesh of Christ 17:4
[T]he Apostles took up her body on a bier and placed it in a tomb; and they guarded it, expecting the Lord to come. And behold, again the Lord stood by them; and the holy body having been received, He commanded that it be taken in a cloud into paradise: where now, rejoined to the soul, [Mary] rejoices with the Lord's chosen ones. - Gregory of Tours Eight Books of Miracles 1:4
You are she who, as it is written, appears in beauty, and your virginal body is all holy, all chaste, entirely the dwelling place of God, so that it is henceforth completely exempt from dissolution into dust. Though still human, it is changed into the heavenly life of incorruptibility, truly living and glorious, undamaged and sharing in perfect life. - Germanus of Constantinople Sermon I
They speak in glowing terms of the work and mission of Mary in the world as the mother of God and the way through which salvation came into the world. These authors demonstrate a great devotion and reverence for Mary because of her exalted dignity and work. They do not worship her, but they recognize that she is a wonderful example and a person to study.