As the circumcision of the flesh was to the old Covenant, so the circumcision of the heart received in water baptism is to the New Covenant.

Circumcision is an initiation into the Covenant.

Both the old and the New Covenant are ratified through the initiatory rite of circumcision. Abraham and Moses learned that God required each male child to be circumcised in the foreskin of the flesh as a sign of covenant. So necessary was obedience to this initiation that those who did not obey were cut off from God and from His people. 

And God said unto Abraham, Thou shalt keep my covenant therefore, thou, and thy seed after thee in their generations. This is my covenant, which ye shall keep, between me and you and thy seed after thee, Every man child among you shall be circumcised. And ye shall circumcise the flesh of your foreskin, and it shall be a token of the covenant betwixt me and you. And he that is eight days old shall be circumcised among you, every man child in your generations, he that is born in the house, or bought with money of any stranger, which is not of thy seed. He that is born in thy house, and he that is bought with thy money, must needs be circumcised: and my covenant shall be in your flesh for an everlasting covenant. And the uncircumcised man child whose flesh of his foreskin is not circumcised, that soul shall be cut off from his people; he hath broken my covenant (Genesis 17:9-14). 

Under the old Covenant every male was circumcised -and thus separated unto the Lord-regardless of the state of his heart. The reality of this sanctification could only be effected by Christ. Therefore, Christian initiation (baptism) can-indeed, must-involve heart reality in addition to external rite.

Circumcision is the seal of faith.

Abraham had already been justified because he had believed God. Righteousness had been imputed to him on the basis of his faith. But God required a further step, a sign of the covenant. He was to bear in his own body a personal reminder of his relationship to God. Similarly, under the New Covenant, justification is on the basis of faith. But the gospel requires us to go beyond believing to baptism-“he that believeth and is baptized shall be saved” (Mark 16:16). 

And he received the sign of circumcision, a seal of the righteousness of the faith which he had yet being uncircumcised: that he might be the father of all them that believe, though they be not circumcised; that righteousness might be imputed unto them also (Romans 4:11). 

 Circumcision is a mark of belonging.

Natural and spiritual Israel share in having a special token of membership in the redeemed community. God sets aside as His own possession those He has selected and called. For natural Israel this was circumcision of the flesh; for spiritual Israel it is the circumcision of the heart. In either case, the people of God were set apart to become a praise in the earth-this is the meaning of the word “Jew.” 

For in Christ Jesus neither circumcision availeth anything, nor uncircumcision, but a new creature. And as many as walk according to this rule, peace be on them, and mercy, and upon the Israel of God (Galatians 6:15, 16). 

(Note: In this context, Paul is contrasting physical circumcision with real spiritual change, cf. Romans 2:28, 29.) 

God had a reason for adding circumcision to the covenant, It was a visible sign to the believer and to the nations that he belonged to God and was bound to Him.