This of course means coming to the realization of one's sinful nature and placing one's faith in the MESSIAH for one's salvation ---- and not on trying to keep the LAW and not by making animal sacrifices.
All should remain aware that we are to remain obedient to the will of God. Very early on this raised the question, "What is the will of God?" We were given the Ten Commandments, but with each Commandment, more questions arose. The Law grew around our (mankind's) questions.
What seemed to happen at this point is that when The Law was broken, punishment ensued, and along with that, stigma. Jesus shook his head at that, announcing, Sins are forgiven. I am sure he did not mean, "Sin is without consequence", but I do think his intent was that punishment and stigma need not be a part of that consequence.
It should also be kept in mind the symbolism Jews used to assure the people their sins were indeed forgiven and remembered no more. Temple sacrifice was a statement of wrong-doing, a desire to do better, and the belief that God, indeed, forgives sin. By the way, animal sacrifice was not a requirement for the forgiveness of sins.