For a Jew, the Passover meal was a personal participation in the Exodus throughout all time.
For seven days you will eat unleavened bread, and the seventh day will also be a festival to the LORD. Unleavened bread may be eaten during the seven days, but nothing leavened and no leaven may be found in your possession in all your territory. And on that day you will explain to your son, ‘This is because of what the LORD did for me when I came out of Egypt. (Exodus 13:6-8)
For all time, a Jew who celebrated the Passover would explain to his son that the Lord brought him - him personally - out of Egypt. The passover was his personal participation in the Exodus from Egypt.
Remember that Jesus was was the new Moses, who was to lead a new Exodus.
About eight days after he said this, he took Peter, John, and James and went up the mountain to pray. While he was praying his face changed in appearance and his clothing became dazzling white. And behold, two men were conversing with him, Moses and Elijah, who appeared in glory and spoke of his exodus that he was going to accomplish in Jerusalem. (Luke 8:28-31)
People miss that little phrase, which is recorded only in Luke’s version of the transfiguration, that Jesus was speaking with Moses and Elijah about a new exodus.
Jesus was instituting a new exodus from slavery to sin, and his exodus would include the return of the manna from heaven, the miraculous bread which came down from heaven every night and gave the Israelites life.
We have to read Jesus’ words, “Do this in rememberance of me”, with the eyes of a Jew who celebrated the passover as a personal participation in the Exodus, concious of the fact that Jesus was the new Moses who was instituting a new exodus. And we have to remember that Jesus said those words at that very same Passover meal.
When Jesus (who is God) sits down at the passover meal on the night before he was to die and says, “Do this in rememberance of me”, he echo’s the words he himself (as God) had given gave to Moses thousands of years prior.
Just like the old Passover was a rememberance - a personal participation for every Jew in the first exodus - the new Passover done “In rememberance of me” is a personal participation for every Christian in the new exodus - the passion, death and ressurection of Jesus Christ.
-Tim-