Brothers and sisters, glory and honor and peace for everyone who does good, the Jew first and also the Greek. For God shows no partiality. All who have sinned apart from the Law will also perish apart from the Law, and all who have sinned under the Law will be judged by the Law. For it is not the hearers of the Law who are righteous in God’s sight, but the doers of the Law who will be justified. When Gentiles, who do not possess the Law, do instinctively what the Law requires, these, though not having the Law, are a Law to themselves. They show that what the Law requires is written on their hearts, to which their own conscience also bears witness, and their conflicting thoughts will accuse or perhaps excuse them on the day when, according to my preaching of the good news, God, through Jesus Christ, will judge the secret thoughts of all.
C.S. Lewis, in the first five chapters of his book Mere Christianity, gives a great and logical explanation of how all of us have a moral compass, and how that moral compass was put in there by God Himself.
In the Epistle passage above, Saint Paul talks about all of us having a Law of God in our hearts. Some of us know it a bit more explicitly because we believe and follow God. And basically all of us know it because we were created by Him and the Law was put into our hearts. We can call this law conscience or moral compass or natural law.
The Law of God is the Law that was given to the people of Israel by God through Moses on Mount Sinai. I think it is a common misconception that Moses received only the Ten Commandments. On Mount Sinai Moses received the whole Law, all of the commandments.
This Law guided the people of Israel in every aspect of their life. This Law was given to them for only one purpose - help them prepare the rest of the world for the coming Messiah. And this Law is the revelation from God, but not an end in itself.
Another popular misconception is that Christ abolished this Old Testament (Covenant), when He established a New Covenant with His creation. It is only partly true. Christ Himself says, "Do not think that I have come to abolish the Law or the prophets. I have come not to abolish but to fulfill" (Matthew 5:17). Orthodox Christian teaching is that Christ is the only one ever to fulfill the Law fully and completely.
Does the Old Testament Law still apply to Christians? Yes and no. We do not circumcise our male infants anymore, only because circumcision was a physical sign of a man belonging to God. Saint Paul talks about circumcision of the heart (Romans 2:17-29), meaning people who follow the commandments and will of God belong to Him. We do not to physically mark ourselves anymore. We do not make sacrifices like the people of the Old Testament did, because Christ became the last and ultimate sacrifice that we ever needed. But we still offer a bloodless sacrifice every Divine Liturgy.
In the above passage Saint Paul also talks about the Gentiles who do not possess the Law, but still do it. The Gentiles are those who have not yet come to believe in the One True God. Yet they follow the Law because it is part of their composition, because God has written His Law on the hearts of each. This Law is what we call conscience or moral compass. It is not as full of a revelation as the Law of Moses, but it is still enough of a revelation for people to have a capacity to make the right choices.
Before the Incarnation, God revealed Himself to humanity through the Law, nature, philosophy, etc. However, these revelations were fulfilled in the coming of Jesus Christ, the Only-begotten Son of God, in the flesh. He has revealed God to us as fully as we need and can comprehend. He has shown to us Who God is and what He does.
Now, we may still look to nature, natural law, philosophy, science to find God, but if our search does not end in Jesus Christ, then our search is incomplete. God wrote His law on our hearts so that we would constantly look for Him and be guided to Him. And since Christ is the fulfillment of God's Law, He is also the fulfillment of our search.
Yours in the Lord,