Saint John Paul II included the institution of the Eucharist as one of the Luminous Mysteries of the Rosary. Mary is the "Eucharistic Woman" because of her interior attitude.
The Eucharist has a sacrificial dimension: it is a memorial of the death and Resurrection of Jesus. We should live the Eucharist with the same attitude that Mary had at the foot of the Cross. On Calvary, Jesus actually asked each one of us to "Behold [our] Mother."
The Eucharist is also an act of praise: Let us live it in imitation of Mary's Magnificat!
Finally, Pope Emeritus Benedict XVI insists on the fact that since Mary is the All Beautiful, in whom the splendor of God's glory shines forth, our assemblies should reflect the beauty of the heavenly liturgy as a faithful mirror of Heaven.
Translated from: Marie de Nazareth website