(Because there are four parties included in this verse, there are four viewpoints or aspects that I feel I should address here) :
Firstly Christ has dealt with the sin question and became sin for us. He has taken upon himself that which has marred the image of God, as defined by God's perfect character in the ten commandments. The Son of God has taken on the guilt, shame, grief, separation from the Father, and all the suffering of man upon himself. He has taken all this and most importantly he has taken all the temptations that we would bear, upon his own fully human frame. He has endured all this in weak, mortal flesh, and experienced those temptations as we would experience them. While here in this world, he has given all of himself to us during his life and has taken all that we are, upon himself in his death. He has done all this and has overcome.
Christ has fulfilled his role as the lamb of God and brought to an end the requirements, of the sanctuary service that pointed to him. He has made redundant those rituals, which became a stumbling stone for his people.
Secondly, the law encapsulated in ceremonies, instead of reminding the sinner of his sin, had become a mask by which the sinner thought he could cover his un-penitent heart. The covenant of faith with Abraham had been forgotten and the law of ordinances which was intended to remind them, became an outward form, a mindless ritual for the unconvicted soul. The death of the innocent animal had lost all meaning, and so in the mind of the sinner, instead of the sacrifice being an act of divine mercy granted by Yahweh to the failing one, to remind them of the Savior to come: Instead of the ritual being an act of faith, whereby symbolically the merits of the innocent were transferred to the sinner, the ritual began to resemble a bloodthirsty pagan sacrifice, whereby the unpenitent hand holding the bloody instrument wielded itself as though it were the means of salvation.
Had God's people approached their maker with eyes of faith, they would have been further awakened by the ordinances, being instructed by the ceremonies and devotions of the priest; if they emulated the spiritual precepts that fashioned these outward practices, in their own lives, they would have heeded the call to love, justice, and mercy. But instead, their hearts became benumbed and indifferent towards their redeemer. And yet God's people were required to be his representative to the rest of the world.
Thirdly, for the Gentiles, the main focus was the things of this life, and so the eternal aspects of the Jewish rituals would have been meaningless to them. But for the gentile, the idea of forgiveness implies that there is someone to fear, and the pagans of the Roman era tended to disregard the idea that the gods were to be feared, and those that did look upon them with fear were regarded as 'superstitio ' or superstitious. The relationship with the gods, therefore, was considered to be mutually beneficial, and through philosophy, as well, the goal was wisdom in self-direction and self-reliance.
The Gentile had no other one he could look to, apart from himself, who truly represented his innermost need. All were trapped in sin, Jew and Gentile alike. For Gentiles, the Jews had in effect become the hypocrites, the false shepherds. For some of the Jews, the only apparent evidence of their purity was not that they embodied the faith of Abraham, but rather that they kept themselves separate from the 'unclean' Gentiles, and so did not associate with or even try to convert them.
The idea of perfection and faithfulness to a single God only was foolishness to the Gentile mind, which attempted to downplay the severity of the fallen human condition. However, their consciences were still convicted for their failings, their thoughts accusing or else excusing one another. (Rom 2:15)
The mindset of the Jew was to focus on religious rules that gave structure and a sense of security to everyday life. However, the law of ordinances became a stumbling block for those that depended on it; and a wall that separated, for those outside the ceremonial sanctuary system. And yet the Gentiles, many of them had their own rituals, their own animal sacrifices, their own ceremonies involving the shedding of blood. But to even think that a person could satisfy the gods without a bribe (which was always by the works of his own hands); Or, that is, to even contemplate the idea of bridging the heavenly chasm to a righteous God, who does not accept bribes (Deut 10:17), would have been beyond imagination to the Gentile.
The New Man:
But Christ has broken down the dividing wall that separated, by fulfilling the Law, in his own body, both the moral and the ceremonial law, being the perfect and unblemished lamb of God. He has brought an end, through the sacrifice of himself, the ceremonial law, while confirming the validity and precepts of the moral Law by his ability to keep God's Ten Commandments, effectively restoring the image of God to the frame of man.
Christ has in himself declared it possible to be free from sin. He has become the ideal also for the Gentile, that seeks such freedom and the guiding influence of a life lived in faith and perfection.
For the Jew, the law was meant to be a pattern upon which to build faith, but the law ended up being a substitute for faith instead. As the apostle Paul had said, “Is the law then against the promises of God? God forbid: for if there had been a law given which could have given life, verily righteousness should have been by the law.” — Galatians 3:21 (KJV).
For the Gentile who was inwardly seeking an ideal to rest his faith upon, he had no firm foundation while he rejected the forms and apparent restrictions of the law.
But in Christ we have the very Law of God embodied in the life of Christ, our ideal, who has done so, not by any appointment to Levitical services, but by his walk of perfect faith in the eternal Father.
Who is made, not after the law of a carnal commandment, but after the power of an endless life. — Hebrews 7:16 (KJV)
We have one who has broken down the hostility, that is, the law of directions in fleshly forms and ceremonies, creating one new man, that has met the requirements of the Law by faith, so making peace. (See Eph 2:15)
We now have One whom we can emulate, as we walk in his footsteps, following the Lamb wherever he goes, being guided and joined together by the Holy Spirit, we now have new life in Christ, both Jew and Gentile. (See also vs 16-22).