Every Saturday in the Catholic Church (provided there is no other feast of greater importance) is dedicated to the Blessed Virgin Mary. A priest may celebrate a special “votive” Mass on Saturday morning in honor of Our Lady.
Venerable Fulton Sheen, for example, insisted that priests celebrate Mass on Saturdays in honor of the Blessed Virgin, which he took very seriously.
Our Lady of Fatima requested that the faithful honor her on the First Saturday of each month.
But why Saturday?
Saturday is the day when creation was completed; therefore it is also celebrated as the day of the fulfillment of the plan of salvation, which found its realization through Mary. Sunday is the Lord’s Day, so it seemed appropriate to observe the preceding day as Mary’s day. In addition, as Genesis describes, God rested on the seventh day, Saturday. The seventh day, and the Jewish Sabbath, is Saturday; we rest on Sunday, because we celebrate the Resurrection as our Sabbath Day. In parallel, Jesus rested in the womb and then in the loving arms of Mary from birth until she held His lifeless body at the foot of the Cross; thus the God-head rested in Mary.
The Vatican’s Directory on Popular Piety supplements the above explanation and gives this account:
Saturdays stand out among those days dedicated to the Virgin Mary. These are designated as memorials of the Blessed Virgin Mary(218). This memorial derives from carolingian time (ninth century), but the reasons for having chosen Saturday for its observance are unknown. While many explanation have been advanced to explain this choice, none is completely satisfactory from the point of view of the history of popular piety.
Prescinding from its historical origins, to-day the memorial rightly emphasizes certain values “to which contemporary spirituality is more sensitive: it is a remembrance of the maternal example and discipleship of the Blessed Virgin Mary who, strengthened by faith and hope, on that great Saturday on which Our Lord lay in the tomb, was the only one of the disciples to hold vigil in expectation of the Lord’s resurrection; it is a prelude and introduction to the celebration of Sunday, the weekly memorial of the Resurrection of Christ; it is a sign that the “Virgin Mary is continuously present and operative in the life of the Church.”
Popular piety is also sensitive to the Saturday memorial of the Blessed Virgin Mary. The statutes of many religious communities and associations of the faithful prescribe that special devotion be paid to the Holy Mother of God on Saturdays, sometimes through specified pious exercises composed precisely for Saturdays.
Saturday is a great day to honor our Blessed Mother and if we are not able to go to morning Mass where it is offered, we can always pray a rosary or another Marian prayer to honor her.
She is our spiritual mother and deserves our love and devotion (as do all mothers) and so dedicating an entire day of the week to her is most fitting.