This title penetrates the mystery itself of the Eucharist, and when well understood, manifests to us the most important part granted to Mary in the economy of the Holy Eucharist.
If we have thoroughly seized Pierre Eymard's thought we understand that she is, first, the Mother of Jesus, giving to the Word her most pure blood, which was changed on the day of the Incarnation into His own Body, into His own Blood, in order to consecrate it later, on the night of the Last Supper, into His Sacrament of Love.
Our Lady of the Blessed Sacrament is Mary receiving in quality of universal dispensatrix of grace, the full and absolute disposition of the Eucharist and the graces that It contains, because this Sacrament is the most efficacious means of salvation, the fruit par excellence of the Redemption of Jesus Christ. To her, consequently, it belongs to make Jesus in the Sacrament known and loved; to her it belongs to spread the Eucharist throughout the world, to multiply churches, to raise them in infidel lands, and to defend faith in the Eucharist against heretics and the impious; to her it belongs to prepare souls for Communion, to rouse them to make frequent visits to Jesus, and to assist zealously at the Holy Sacrifice of the Mass. She is the treasure-house of all the graces comprised in the Eucharist, both those that prepare the soul for It and those that flow from It.
— Month of Our Lady of the Blessed Sacrament by St. Peter Julian Eymard
From: https://www.catholicculture.org/culture/liturgicalyear/calendar/day.cfm?date=2016-05-13