All references are to the New International Version Bible.
"…The Lord Jesus, on the night he was betrayed, took bread, and when he had given thanks, he broke it and said, 'This is my body, which is for you; do this in remembrance of me.' In the same way… he took the cup, saying, 'This cup is the new covenant in my blood; do this, whenever you drink it, in remembrance of me.' " (I Cor. 11:23-25, italics added) The Lord's Supper was instituted by our Lord at the Passover time. Jesus knew he was the antitype of the Passover lamb, He was to fulfill what the Passover lamb had pictured. It had even been revealed to John the Baptist that the Messiah was to fulfill the symbols used in the Old Testament; and he said, "Look, the Lamb of God, who takes away the sin of the world!" (John 1:29) Jesus' disciples would no longer celebrate the Passover and remember Israel's deliverance, because the symbols of the Old Testament were now becoming reality. But the Lord did give his followers a special way to remember His sacrifice.
We know that when Jesus gave His disciples the bread and wine, He had not yet been sacrificed. So the bread and wine they received could not have been his actual flesh and blood. And today the body and blood of our Lord do not have to be mystically recreated so that believers can partake of them in order to be cleansed from sins.
We know that "the blood of Jesus, his Son, purifies us from all sin." (I John 1:7) But does that mean we need to continually actually drink Jesus' blood in order to be cleansed of sin? John answers this two verses later, where he says, "If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness." (I John 1:9) It is not that we need to receive the actual blood and body of Jesus to be cleansed from sin, but that we need to, in our hearts, by faith, receive the justification which He offers us. Paul says, "The death he died, he died to sin once for all…" (Rom. 6:10, italics added) And in Hebrews we read, "Nor did [Jesus] enter heaven to offer himself again and again… Then Christ would have had to suffer many times since the creation of the world. But now he has appeared once for all… to do away with sin by the sacrifice of himself." (Hebrews 9:25. 26, italics added)
So we see that Christ's blood was shed only once, His body sacrificed only once, and that was enough. The bread we take at the Lord's Supper is a symbol of His perfect, sinless body, which He gave as a ransom. When we partake of that, we are again accepting His sacrifice, receiving the life, the justification He gives us. When we take the fruit of the vine at the Lord's Supper, it is a symbol of His shed blood, which takes away our sins, and of the new life He gives us. We remember His great love and sacrifice and renew our faith in Him. In addition, those who have given their hearts fully to the Lord in consecration celebrate their oneness with Him, and with other Christians, and their participation in His suffering. "For it has been granted to you on behalf of Christ not only to believe on him, but also to suffer for him." (Phil. 1:29) We especially remember this newness of life and rejoice that all who have ever lived have been bought with His blood, and they will someday partake of the life Jesus secured for them.