When God enters into covenants with His people, making promises of redemption to them, His pattern is to attest to the authenticity of the covenant by giving some kind of external sign. For instance, when He promised Noah that He would never destroy the world again through a flood, God set His bow in the sky. That bow was a visible sign that confirmed the promise of God for the future of this planet. He was saying that every time we see a rainbow, we should be reminded that God has promised never to destroy the world again with a flood.
In a similar manner, after instituting His covenant with Abraham, God gave Abraham and his descendants a sign of their membership in the covenant: circumcision. This sign had a dual significance. On the one hand, the cutting of the foreskin was a sign that God was saying, “I am cutting you out from the rest of fallen humanity and consecrating you as a nation to Myself.” At the same time, the sign was a testimony by the people, saying, as it were, “O God, if I fail to keep the terms of this covenant, if I fail to be faithful to You in this covenant relationship, may I be cut off from all of the benefits of Your covenant promises.” So circumcision symbolized both the blessings and the curses of God’s covenant with Abraham.
The rite of circumcision was given for all generations of Israelites as the sign of the old covenant. That’s why, if we were to ask a Jew to identify the sign of God’s covenant with His people, he would say that the sign is circumcision.
Just as circumcision was the sign of the old covenant, baptism is the sign of the new covenant. In a very real way, what circumcision was to the Old Testament, baptism is for the New Testament. We see this close connection in Paul’s letter to the Colossians. He writes:
For in him the whole fullness of deity dwells bodily, and you have been filled in him, who is the head of all rule and authority. In him also you were circumcised with a circumcision made without hands, by putting off the body of the flesh, by the circumcision of Christ, having been buried with him in baptism, in which you were also raised with him through faith in the powerful working of God, who raised him from the dead. And you, who were dead in your trespasses and the uncircumcision of your flesh, God made alive together with him, having forgiven us all our trespasses, by canceling the record of debt that stood against us with its legal demands. This he set aside, nailing it to the cross. He disarmed the rulers and authorities and put them to open shame, by triumphing over them in him. (2:9–15)
Paul here tells a body of Gentile believers who have received New Testament baptism that those who are believers have received an internal circumcision. They have a circumcision of the heart, so it is proper and appropriate for them to have the sign of the new covenant, which points beyond itself to all of the benefits of Christ.
R. C. Sproul, What Is Baptism?