The symbolism behind the second cup
With the last of the four cups served at Passover, we read, ‘In the same way, after the supper he took the cup, saying, "This cup is the new covenant in my blood, which is poured out for you.’ Jesus said, ‘This cup is the new covenant in my blood.’
His death establishes the New Covenant
This reminds us that in His death the Lord was establishing a new covenant with us. Now ‘covenant’ is a very relational term. Think of two lovers coming together in the covenant of marriage. What Christ is doing for us draws us into a covenant with one another, but it also draws us into a covenant with God. The allusion harkens back to texts like, Jeremiah 31:31-34, Ezekiel 36:26-27, and others, where the Lord promised to make a new covenant with His people and give them a new spirit and heart that would urge them enable then to walk with Him, and walk in His ways.  That is the Spirit calling from within us. This is fulfilled in the giving of the Holy Spirit to indwell us. And whereas under the Old Covenant, faithfulness was encouraged upon God’s people from the outside, under the New Covenant the urge to be faithful comes from within us. And this covenant was sealed with Christ’s blood.
Communion serves as a memorial to what Christ has done
Jesus said, ‘do this in remembrance of me.’ We all have trouble remembering things. Sue and I have spent half an hour looking for the remote control, our keys, our glasses. I have trouble remembering telephone numbers, and names, and birthdays, and anniversaries. Just ask Sue. It is kind of interesting that of all the Gospel writers, Luke is the only one who includes the words, ‘do this in remembrance of me,’ in his Gospel. Matthew, Mark, and John all forgot to include them in their accounts. Only Luke remembered Jesus saying these words. And Luke wasn’t even at the Last Supper. Some one, maybe the Spirit, must have told Luke what Jesus said.  Why does only Luke have Jesus telling us, ‘Do this in remembrance of me.’ Why didn’t the men who were there, Matthew, John, mention them? Well, the answer is that even the best of us are a forgetful people.
What should we remember?
We are a forgetful people. But the Lord established the practice to help us remember. But what exactly does it mean to remember Him? What does He want us to remember? What are we supposed to not forget? The words direct out attention to: to the benefits Christ brings to our needs, to our coming future with Him, to the rewards participation in the meal bring to us, assurance and the sense of oneness with one another. But most of all Jesus wants us to remember Him, be aware of His caring presence, and love for us.
The Messianic Banquet
Let me just conclude by saying this. Communion, like Passover, has elements of past, present and future. Communion in particular is very forward looking. There will be a new Exodus so to speak, when the Lord comes to bring us home. Jesus told us, ‘I will not eat it again until it finds fulfillment in the kingdom of God’, and ‘I will not drink again of the fruit of the vine until the kingdom of God comes.’ And He is referring to the Great Messianic Banquet which unveils our eternity. As we go through life in the here and now, the New Covenant has been established. The Spirit has arrived. But the world, and we ourselves, have not yet been made perfect. That awaits the day our Lord’s returns.