I am going to respond to this question using the works of our Holy Father especially, “What it Means to be a Christian” along with a few of my own thoughts. I hope that my thoughts reflect what the Pope meant to say.
In several works of our Holy Father that I have read he makes a point I think is very important, namely, we cannot fully understand the New Testament without have a knowledge of the Old Testament. The Old points to the New and both find their fulfilment in Christ Jesus. In any discussion about the Mosaic Law, I think it is important to remember what was at the heart of “The Law” - the Love of God as expressed in the Sinai Covenant. Israel saw that it could filfill the obligations of the covenant by keeping “The Law”. The book of Leviticus states this clearly and Christ quoted Leviticus when he was ask by a young man what he must do to be saved. But in its human expression the Mosaic Law was incomplete and how it was being lived was profoundly flawed. I believed this lead to the strong criticism Jesus directed towards the religious leaders of his time and is reflected in the writings of St. Paul and his criticism and apparent rejection of the Mosaic Law.
Our Holy Father also points out, or re-states clearly, that the Old Testament (Covenant) points to the New and that we are a New Covenant people. This covenant was established by Christ at the Last Supper with the institution of the Eucharist and sealed in the blood of his paschal sacrifice. Through baptism, we enter into this new covenant and through the Eucharist we become one with the Body of Christ and and participate fully with the Body of Christ - the Church. For me, this change everything and we (the Church) are no longer an Old Covenant people and are no longer bond by observance of its “Law”.
God deals with us in the reality of our normal daily life and as I study the Acts of the Apostles and the letters of St Paul, I become more convinced that we find God, through His Holy Spirit, guiding the Church through a deeper understanding of her nature and mission of what it means to be a New Covenant people. But this understanding didn’t just happen but developed with time, experience, debate and most importantly through prayer. We can read about this struggle in Acts and the events leading up to the Council of Jerusalem, the Council itself and how the decisions of the Council was lived out in the early Church. In Paul’s letter we can read how the Church was moving beyond its understanding as being just the perfection of the Old Covenant and whose mission was primarily to God’s chosen people, the Jews and thus still under the obligation to live and perfect the Mosaic Law, to a broader understanding of what it meant to be a New Covenant people.
However, this did not just happen and all all were under the guidance of the Holy Spirit there were serious tensions, debates and bitter disagreements in this process. Too often this has been over simplified as a struggle of Paul against the rest of the Church or Paul against James (sometimes Peter) and the Church of Jerusalem.