In the same manner He also took the cup after supper, saying, “This cup is the new covenant in My blood. This do, as often as you drink it, in remembrance of Me.” (I Corinthians 11:25 NIV)
Taking the wine of communion, like the bread, must be done in remembrance of Christ. A Christian taking the Lord’s supper needs to be constantly focusing on Christ’s sacrifice, remembering His blood that was shed for us. Christ’s death on the cross for our sins is the sole basis for our salvation. Believers have entered into a new covenant with Christ. It is not a covenant whereby we purchase our own salvation with our good works, rather, it is a covenant whereby we are saved by the blood of Christ. Those who are partakers of the new covenant are spiritually changed by the Holy Spirit to desire good and not evil.
Here is one of the many predictions of the New Covenant that is found in the Old Testament:
But this is the covenant that I will make with the house of Israel after those days, says theLord: I will put My law in their minds, and write it on their hearts; and I will be their God, and they shall be My people. 34 No more shall every man teach his neighbor, and every man his brother, saying, ‘Know the Lord,’ for they all shall know Me, from the least of them to the greatest of them, says the Lord. For I will forgive their iniquity, and their sin I will remember no more.” (Jeremiah 31:33-34 NIV)
The new covenant, as explained here, is something that happens in the minds and hearts of believers. It is a complete change brought about by the Holy Spirit, resulting in a direct relationship with God and forgiveness of sin. The New Covenant was promised first to the Jewish people, but later, when Jesus came, it was revealed that the New Covenant was for all mankind, including gentiles. Anyone who believes in Jesus Christ is saved by the sacrifice of His blood, and is regenerated by God.