Orthodox Christians bless, venerate, and honor Mary, but we never worship her.
Part of the confusion about the worship of Mary stems from the very idea of worship itself. In modern churches when one talks about worship they usually mean the singing that takes places before the sermon. When a visitor hears us singing about Mary, they associate that singing with worship of Mary. But in the Orthodox church, worship is understood as sacrifice. When we offer the Eucharist we participate in the sacrifice of the body and blood of Jesus. Orthodox would never offer a sacrifice to Mary.
We honor Mary due to her relationship with Christ, it is never done in isolation or based on her own merit. In the icons of the church will rarely, if ever, see Mary depicted by herself. She is always shown with Christ.The most common image is Mary holding Christ with her hand pointing to Him, directing the faithful to look unto Christ for salvation.
In Luke, we read,
A certain woman from the crowd raised her voice and said to Him, “Blessed is the womb that bore You, and the breasts which nursed You!” But He said, “More than that, blessed are those who hear the word of God and keep it!”
Mary is not honored solely based on the fact the she physically gave birth to or nurtured Jesus. She is honored because she heard the word and kept it. It is her life of being completely surrendered to the will of God that she is honored. While giving birth to Christ is Mary’s own unique experience, her example of submission can be followed by all Christians.
The Orthodox church lives out the scripture,
“henceforth all generations will call me blessed.”
There has been much debate in recent centuries about the level of veneration that is due to Mary, largely due to the fear of going too far. The unfortunate result has been to not honor Mary at all. In fact, the Rev. Billy Graham has said repeatedly, “We evangelical Christians do not give Mary her proper due.” Many modern Christians look at Mary as a distant historical figure but for Orthodox Christians she is a present, living example in our worship of the one God. Since the beginning of Christianity to the present day we have never ceased to honor Mary.
Quotes from Early Christians:
For whereas Eve, yet a virgin and undefiled, through conceiving the word that came from the serpent, brought forth disobedience and death; the Virgin Mary, taking faith and joy, when the Angel told her the good tidings that the Spirit of the Lord should come upon her, and the power of the Most High overshadow her, and therefore the Holy One to be born of her should be the Son of God, answered, Be it don to me according to thy word. And so by means of her was he born, concerning whom we have shown so many Scriptures were spoken; through whom God overthrows the serpent, and those angels and men who have become like to it, and on the other hand, works deliverance from death for such as repent of their evil doings and believe in him - St. Justin Martyr, Dialogue with Trypho (c. 160 A.D.)
Just as Eve, wife of Adam, yet still a virgin, became by her disobedience the cause of death for herself and the whole human race, so Mary, too, espoused yet a Virgin, became by her obedience the cause of salvation for herself and the whole human race.... And so it was that the knot of Eve's disobedience was loosed by Mary's obedience. For what the virgin Eve bound fast by her refusal to believe, this the Virgin Mary unbound by her belief. - St. Irenaeus, Against Heresies (175-185 A.D.)
The whole race of man upon earth was born from Eve; but in reality it is from Mary the Life was truly born to the world. So that by giving birth to the Living One, Mary became the mother of all living - St. Epiphanius, Against Eighty Heresies, 78,9 (c. 374)