It has to do with putting off the old man of sin, where we walked in the likeness of Adam. We have been remade in Christ, and should walk after Him. This can be painful (like crucifixion) - e.g. turning the other cheek to someone who deserves a beating can be hard, but this is an example of crucifying the flesh - submitting to God, rather than our evil, selfish desires.
Romans 6:3-7
Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death?
Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin.
For he that is dead is freed from sin.
Circumcision of the heart is a similar metaphor. Putting off the uncleanness and sins of the flesh through the circumcision of Christ. Again, the metaphor indicates pain is involved in causing the flesh to submit, but for the overall benefit of the believer by being in covenant with Christ and inheriting eternal life.
Colossians 2:
In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ:
Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead.