For the Jews, the Mosaic Law was that law which was given to Moses by God, and was the ultimate arbitrator of how they were to live their lives, both civilly and religiously. By healing the leper, Jesus shows us that he goes beyond the law.
As we see in the first reading, leprosy was one of the reasons by which one could be declared ritually unclean. Being declared unclean not only prevented you from entering into the temple to worship God, but also had consequences that reached into your daily life. Those publicly declared unclean were shunned by family and friends, and in some cases were required to leave the camp or town until you were able to be cleansed of what ever made you unclean.
If you think about it, this makes sense from a medical standpoint. Diseases, such as leprosy, were completely untreatable through normal means at that time. They didn't have the medical knowledge or technology that we have today which enable us to cure many diseases that were nearly always fatal. To prevent the spread of the diseases, the infected person was cast out of the community until death or recovery from the disease, which ever came first. Once the person was healed from the disease, they could undergo a ritual purification which included a sacrifice. They could then be readmitted to their community and family. While they might not have understood everything about how diseases spread, they obviously understood the basic concept of isolation preventing the spread of disease.
Another way to become ritually unclean was either to touch or be touched by someone who was considered unclean. By Our Lord touching the leper, he also would have been considered ritually unclean, and may have suffered the same fate of being cast out of the community. Instead of Jesus receiving the disease from the leper, Our Lord was able to heal the leper, removing the disease and all effects that come from it. Rather than being made ritually unclean by the leper, Our Lord went beyond the Mosaic law by washing the leper clean, both from his disease and from his ritual impurity.
The leper provides for us the example of how to approach Our Lord with humility. All of us have our uncleanliness, our sins that we need to ask for the cleansing of Christ to come upon us and heal us. The leper was willing to come to Our Lord and say to Him, “If you wish, you can make me clean,” and Jesus responded, “I do will it. Be made clean.” We also need to come before the Lord and ask Him to make us clean.
We do this through regular reception of the Sacrament of Confession. How often is regular? At a minimum, we are required every time we know that we have a mortal sin on our soul. These serious sins cut us off from God, a separation that can only be healed through Confession. We are also required by the Church to receive this Sacrament at least once a year, even if we haven't committed a mortal sin in that time.
Of course, once a year is the bare minimum. We are encouraged to receive this Sacrament more frequently. Ideally, we should confess our sins and receive the cleansing of Christ's forgiveness and absolution at least once a month to provide us with the grace to overcome those sins which we seem to repeat over and over again. I frequently call these our “favorite” sins, because we seem to enjoy committing them repeatedly. Even if we only have venial sins on our souls, the graces which come through the Sacrament of Reconciliation will help to cleanse us from our sinfulness.
When we approach the Sacrament and hear the words of absolution, our sins are forgiven and our souls have been cleansed, much as the serious disease of the leper was healed. Like the author of the psalm we heard, God will take away the guilt of our sins, making us truly blessed in His eyes. As the leper did following his healing by Our Lord, we should rejoice in the forgiveness of our sins through the mercy of God and the cleansing of our souls.