Verse 15 tells us what was on Christ's mind, and again, it was not the disciples' sins. Instead, the Son of God had been fervently looking forward to this special occasion - this fellowship - with those whom the Father had given Him (see also Matthew 26:18-29; Mark 14:13-25). Like the Exodus Passover, this Passover was about eating. However, the New Testament Scriptures place the emphasis on the bread and wine. The bread and wine are not new symbols, though, but the original elements of the fellowship meal between Melchizedek and Abraham (Genesis 14:18) on the eve of a historic covenant (Genesis 15). In like manner, this Passover was a fellowship meal on the eve of the sealing of a much-anticipated covenant.
There is not time to explore this completely, but notice that Jesus says that the Passover will not be fulfilled until the Kingdom of God. It is easy to read right over that, but it is a critical part of Passover. The sin offering has already been fulfilled (Hebrews 1:3; 7:27; 9:12-14, 26-28; 10:12, 18), but the Passover has not, as it says here. This is because of Passover's theme of redemption, which is actually a process. This is why Scripture speaks of redemption in both the past (Romans 3:23-25; Ephesians 1:7; Colossians 1:14) and future tenses (Luke 21:28; Romans 8:23-25; Ephesians 1:13-14; 4:30). We have been redeemed from the death penalty, but we still need to be redeemed from this corrupted nature that incurs the death penalty (see Titus 2:11-14). God must redeem us from this flesh - this body of death, as Paul calls it - so we can fully manifest the image of our Creator. Thus, our final redemption occurs when we have been resurrected and have fully taken on the incorruptible nature (see I Corinthians 15:50). At that point, Passover will be fulfilled.
Jesus Christ's body is a multi-faceted symbol. Sometimes Christ's body is a symbol of His death, but at other times it is a symbol of life. So, it says here that the Passover bread represents Christ's body. When Jesus uses bread as a symbol for His body, it is a symbol of life, even eternal life. We won't turn to it, but John 6 explains this symbol very clearly. There, Jesus speaks of bread that endures to everlasting life. He speaks of the bread of God, the bread of life, and the living bread. When Jesus says that He is the living bread (John 6:51), it means that His flesh is not merely something that leads to eternal life, but He indicates a body that is alive. As we partake of the bread, we become one with the living Savior.
Let us go a little bit further. This time we are going to turn to Matthew 26, as we continue to lay the foundation for this series on the Passover. Here, on this occasion, we see Matthew's recording of the events that occurred on the last night of Jesus Christ's life—when He had His last Passover meal with His disciples. It was here that He instituted the new symbols representing His body and blood. (Here I mean the "new symbols" for the proper keeping of the Passover.)
Jesus Christ, then, commanded His followers (all who have repented of their sins and, by faith, accepted His blood of the sacrifice for the forgiveness of their sins) to partake of the New Covenant symbols as a solemn memorial of His death. Each of these occasions—that is, when His death is memorialized—is to be a renewal of the New Covenant believer's relationship with God, through the sacrifice of Jesus Christ.