There are different interpretations of Natural Law. For our purpose here, it suffices to distinguish between the two main interpretations that matter.
“Natural Law is carved in our bodies”
Teaching authorities in the Catholic Church and other traditional social circles adhere to the so-called Physical Interpretation of Natural Law. In short it comes to this: a being’s nature, and therefore the law governing it, has been laid into that being’s physical make up.
In this view, the Creator is like a sculptor. God gave us wonderful properties, but we cannot and may not exceed what God has carved into our bodies.
To start with a basic example. Pig’s can’t fly, they can’t ride on bicycles, they can’t produce art or create love poems. These things are simply not in their nature as God created them. Therefore they should not fly, ride bicycles, produce art or create love poems. These things go against the law of their nature.
Human beings too, like pigs, have a physical nature. God has written what they can and can’t do in people’s physical organs. That is where the law of their nature can be found. Now humans have a brain. So, if they want to know what they should or should not do, they should use their intelligence to study their own bodies and decypher natural law as it applies to them.
As to homosexuality, the physical make up of our bodies shows that women are made to have sex with men, and vice versa. So that is Natural Law for them. This law should be followed always and everywhere. “Homosexuality is opposed by the objective impossibility of making the partnership fruitful through the transmission of life according to the plan inscribed by God in the very structure of the human being. Another obstacle is the absence of the conditions for that interpersonal complementarity between male and female willed by the Creator at both the physical-biological and the eminently psychological levels.” Family, Marriage and “De Facto” Unions, Declaration by the Pontifical Council for the Family (2000), § 23.
“Natural Law is our human reason”
However, from the early Middle Ages on, scholars have adopted the so-called Rational Interpretation of Natural Law. They recognised that the distinguishing mark of humans is precisely the fact that they have the faculty of reason. They have intelligence.
When God created humans, he created them “in his own image” (Genesis 1,26). God gave us a mind and free will so that we could, and should, work out actions for ourselves in a responsible fashion. To put it differently: God made us small creators in our own world, responsible to work out what is right and wrong by using our intelligence.
Or to use another comparison, the Creator is like a parent who wants his/her child to do well, to grow, to expand, to become a personality who can responsibly distinguish virtuous from evil actions. The responsible use of their intelligence is the Law of their Nature.
Now this interpretation of Natural Law was first formulated by two of the most eminent theologians in Christian history: Albert the Great and Thomas Aquinas.