Circumcision was a way to set apart God's people from other people of the world. God required Israelite men to be circumcised to show that they were different from the surrounding nations.
"God said further to Abraham, 'Now as for you, you shall keep My covenant, you and your descendants after you throughout their generations. This is My covenant, which you shall keep, between Me and you and your descendants after you: every male among you shall be circumcised. And you shall be circumcised in the flesh of your foreskin, and it shall be the sign of the covenant between Me and you. And every male among you who is eight days old shall be circumcised throughout your generations, a servant who is born in the house or who is bought with money from any foreigner, who is not of your descendants. A servant who is born in your house or who is bought with your money shall surely be circumcised; thus shall My covenant be in your flesh for an everlasting covenant. But an uncircumcised male who is not circumcised in the flesh of his foreskin, that person shall be cut off from his people; he has broken My covenant." (Genesis 17:9-14)
Circumcision was the mark that set apart the Jewish people as people of God's possession.
Medically, the cutting off of the foreskin helps the male to be physically cleaner than someone who is uncircumcised. Removing the foreskin simplifies hygiene during regular bathing.
Due to increased hygiene in a circumcised male, a woman would also benefit from this during intimacy.
So the law on circumcision has a health benefit.
Married couples were considered one flesh (Genesis 2:24). So when a husband is circumcised, the woman is also part of the covenant. Similarly, a daughter is under the rule of her father. So when a father is circumcised, the daughter is also part of the covenant.
Women do benefit from men's circumcision in this way.
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God wanted to correlate the physical act of circumcision to a spiritual lesson. That is, we need to get rid of our fleshly deeds and be faithful to God.
This idea was present in the Old Testament:
"...for all the nations are uncircumcised, and all the house of Israel are uncircumcised of heart..." (Jeremiah 9:26)
God wants us to not be fleshly or worldly, but be spiritual.
Circumcision is the physical act of cutting off the fleshly part of ourselves.
In Christ, the spiritual act of circumcision applies to everyone (both male and female):
"...In Him you were also circumcised with a circumcision made without hands, in the removal of the body of the flesh by the circumcision of Christ; having been buried with Him in baptism, in which you were also raised up with Him through faith in the working of God, who raised Him from the dead. When you were dead in your transgressions and the uncircumcision of your flesh, He made you alive together with Him, having forgiven us all our transgressions, having canceled out the certificate of debt consisting of decrees against us, which was hostile to us; and He has taken it out of the way, having nailed it to the cross." (Colossians 2:11-14)
So by believing in Christ and repenting of our fleshly deeds, we are circumcised by God with true spiritual circumcision.
"But he is a Jew who is one inwardly; and circumcision is that which is of the heart, by the Spirit, not by the letter; and his praise is not from men, but from God." (Romans 2:29)