At the Last Supper, Jesus celebrated the Passover meal with his disciples one last time. The Passover commemorated the “gospel event” of the Old Testament: God’s deliverance of Israel from slavery in Egypt. This was the event that established Israel as the people of God. By participating in the meal, every Israelite was spiritually participating in the Exodus. They could legitimately say, “We were Pharaoh’s slaves in Egypt, but the Lord brought us out of Egypt with a mighty hand.” (Deut 6:21).
But Jesus redefined the meal on the night before his death. He had previously pronounced judgment on Israel, including its leadership and its temple. So now he forged a new covenant that established a new people of God—a people no longer gathered around Moses and the Law, but gathered around himself and his sacrificial death. And this final meal Jesus ate with his disciples enabled them to participate spiritually in the new foundational event of this new people.
Jesus used the bread and the wine of the meal to point to his body and blood. Through the centuries there has been considerable debate about how exactly these elements relate to the physical body and blood of Jesus. The Roman Catholic Church has taught that the elements change (“transubstantiate”) into the actual body and blood of Jesus—something Martin Luther also maintained. Other churches have taught that Christ’s body and blood are united (“consubstantiate”) to the elements, or that the elements are purely symbolic and only prompt the believer to reflect on the death of Jesus.
So what is actually going on during the Lord’s Supper?
If the Passover meal enabled the Israelites to participate in the Exodus in a spiritually real way, the Lord’s Supper does something similar for Christian believers. By faith, this token meal is able to bridge the historical gap between the believer and the foundational event of the Christian faith.
No Israelite thought the lamb they sacrificed and ate morphed into one of the lambs slaughtered that first Passover. But it was an apt way to commemorate and participate in that first Passover. Similarly, the bread and wine that Christians consume don’t change into Jesus who suffered and died in the early first century. But there is a significant spiritual thing happening that is more than just a solemn reflection upon Jesus’ death. Just as the lamb took the Israelite back to the Exodus, so the bread and the wine take the Christian believer back to Jesus’ death.
The elements are a bit like an actor in a film. The actor takes on a particular character for the film, and makes that character come alive for the viewer. The better the actor, the more vivid the presentation. The actor makes the character present to the viewer, who accepts the actor as the character. But at no point does the actor stop being himself and actually turn into the character. On the contrary—he always remains who he actually is. He is merely taking on a role for the benefit of the viewer, who also realizes how the acting role works.
In a similar way, the bread and wine never stop being bread and wine. They do not actually become Jesus, just as Claire Foy does not actually become Queen Elizabeth II, and Robert Downey Jr. does not actually become Iron Man. Nevertheless, in the Lord’s Supper, the elements present Christ to the believer who accepts them by faith. They are fitting symbols—a sacrament—so they present Christ vividly. It’s not that Christ is being crucified all over again. That happened once in the first century, and will never happen again. But they enable the believer to participate spiritually in that foundational event of Christian faith. It’s as though the believer is spiritually transported to the foot of the cross, so that by faith they can say, “Christ body was broken for me, and his blood was shed for me.”
If the Israelite participating in Passover could legitimately say, “I was a slave in Egypt but the Lord brought me out of Egypt with a mighty hand,” then participating in the Lord’s Supper allows the believer to say, “I was a slave to sin, but Jesus saved me by his body and blood.” That’s the essence of the new covenant.
I’ve written a short blog piece at 
With Meagre Powers 