And he took the cup, and gave thanks, and gave it to them, saying, Drink ye all of it; For this is my blood of the new testament, which is shed for many for the remission of sins. (Matt 26:27-28)

And he said unto them, This is my blood of the new testament, which is shed for many.  (Mark 14:24)

Countless animals were killed in Jewish history to provide the blood required for the proscribed sacrifices.  This is because blood is required to remit sin (Heb. 9:22).  However, none of those sacrifices provided the actual blood that was required.  Those sacrifices were only symbolic of the ultimate sacrifice provided by Jesus Christ (Heb. 10:4, 10-14).

In the verses above, we see that His blood was shed “for the remission of sins”.  This was His purpose for us—to take away the sins that would condemn us.

His blood was shed “for many”.  This should not be understood to mean that Jesus only shed His blood for some, but not all.  Rather, the meaning has to do with the effectiveness of His blood to those who believe.  Jesus died for all human beings (John 3:16; 1 Tim. 2:6).  We must remember that “many” can be used in the same sense as “all”.  For example, it would be acceptable to say, “There are many in the world.  All are loved by God.”  Here, “many” and “all” both refer to the entire population.

Jesus’ blood is the “blood of the New Testament”.  “Testament” here should be understood as “covenant” or “contract”.  The new covenant that God makes with all people is that if they place their faith in Jesus’ death as providing full payment for their sins and acknowledge that He rose from the dead, then God will grant them eternal life (Rom. 10:9).  This is literally the opportunity of a lifetime, because none of us are worthy of this!  This is why we should glorify God with our lives, because He provides payment for our sins.  We just have to accept the gift!