“Do this in remembrance of me” means more than “this meal is a memory prompt”. It means more than the sort of trip down memory lane we enjoy with the family photograph album. Instead the word ‘remembrance’ means ‘anamnesis’–a special kind of active and dynamic remembrance in which the event from the past comes alive in the present.
At Passover the Jews believed in a kind of time travel. Through the ritual they were being taken back thousands of years to that night in Egypt where God delivered them from slavery through the death of the Sacrificial Lamb. The time travel also went the other way–the event from the path was brought forward to be experienced in the present. So it is with the ‘anamnesis’ or remembrance of the Eucharist. We are taken through the ritual back through time to the foot of the cross and The once for all sacrifice of Christ on the cross is brought forward into the present moment and its benefits applied to us.
As a result, when Christ says at the Last Supper, “Do this in remembrance of me” he conflates the whole Jewish salvation history from the fall of our first parents through the covenant with Noah, the near sacrifice of Abraham our Father in Faith and the bread and wine offered by Melchizadek. The Passover Lamb is there for Christ himself is the Lamb of God who takes away the sins of the world. 
The remembrance of the Last Supper is, therefore, not simply a memory of Jesus’ last fellowship meal with his disciples, but it is a recognition that this meal is a turning point in time. Because it captures and brings into the present moment the one sacrifice of Calvary, it is the meeting point of the whole of salvation history. It is the end and the beginning. 
Here the maker of the universe gathers all together in a tragic and triumphal harvest. Here all is reconciled. Here the chaos is brought back into its rightful order which is cosmos. Here is the full, final sacrifice eternal in the ages; and the magnificent and humbling beauty of the Catholic faith is that ordinary you and ordinary me can be there on bended knee, our mundane lives caught up in the heart of Light–the still point of the turning world, the harmony of all things and the music beyond our hearing which is the music of the cosmos, motored by the Love that moves the sun and all the other stars.