What does it mean to "Do this in memory of me"?

Last Supper by Duccio di Buoninsegna

Last Supper by Duccio di Buoninsegna

At the Last Supper, Jesus took bread and wine, declared them to be his Body and Blood, shared them with his disciples, and instructed them to “do this in memory of me.”
When we think of a memorial, we normally think of remembering an event or a person in terms of “calling them to mind.” Memorial plaques, statues, or services call to mind significant events in history and those who were involved in them.
Pictures or other mementos of loved ones who have died or who live far away from us help us call them to mind. In this way, these activities are participated in or items are viewed “in memory” of the events or persons they commemorate.
The Holy Mass is a memorial. However, it is not a memorial in the same way as the examples just described. The Mass does more than call to mind the Paschal Mystery – the Passion, Death, and Resurrection of Christ.
If the Mass were only a memorial in the common use of the term, some sort of dramatic reenactment of these saving events in the life of Christ would probably be more appropriate. Instead, the Church has passed down a ritualized liturgical celebration that has been organically developed under the guidance of the Holy Spirit through the centuries.
To understand what the Church means when she refers to the Holy Mass as a memorial of the sacrifice of Christ, we have to understand the scriptural understanding of this word. The Catechism of the Catholic Church explains this as follows:
“In the sense of Sacred Scripture the memorial is not merely the recollection of past events but the proclamation of the mighty works wrought by God for men. In the liturgical celebration of these events, they become in a certain way present and real. This is how Israel understands its liberation from Egypt: every time Passover is celebrated, the Exodus events are made present to the memory of believers so that they may conform their lives to them” (no. 1363; italics in the original).
In the New Testament, and in the time of the Church, the memorial takes on a new and deeper meaning. The Catechism explains, “When the Church celebrates the Eucharist, she commemorates Christ’s Passover, and it is made present: the sacrifice of Christ offered once for all on the Cross remains ever present” (no. 1364).
Here we connect again with the theme of last month’s article: the Holy Mass as a sacrifice because it is the re-presentation and the memorial of Christ’s sacrifice on the Cross. The Catechism refers to the Eucharist as the “sacrificial memorial” of Christ and explains that the Mass is a sacrifice because it is the memorial of Christ’s Passover (cf. CCC, no. 1365).
It is the memorial of this not simply because it calls it to mind, but because the liturgical celebration of the Eucharist makes this event truly present.
Jesus says, “This is my Body and my Blood: Do this in remembrance of me,” affirming the Real Presence of Christ in the Eucharist. He could also say to us, “This is my sacrifice … this is the making present of my offering to the Father for love of you: Do this in memory of me. Allow yourself to be united to my offering as you enter into the Holy Sacrifice of the Mass. Make your own offering in union with mine, so that I may take it for you to the Father.”