What is natural law and why is it important?

That is, what we ought to do is based on what we are.  "Thou shalt not kill," for instance, is based on the real value of human life and the need to preserve it.  "Thou shalt not commit adultery" is based on the real value of marriage and family, the value of mutual self-giving love, and children's need for trust and stability.

The natural law is also naturally known, by natural human reason and experience.  We don't need religious faith or supernatural divine revelation to know that we're morally obligated to choose good and avoid evil or to know what "good" and "evil" mean.  Every culture in history has had some version of the Ten Commandments.  No culture in history has thought that love, kindness, justice, honesty, courage, wisdom, or self-control was evil — or that hate, cruelty, injustice, dishonesty, cowardice, folly, or uncontrolled addiction was good.  Speaking of pagans, St. Paul says that "they show that what the law requires is written on their hearts, while their conscience also bears witness" (Rom 2:15).

The term "natural law" is sometimes misunderstood.  "This law is called 'natural,' not in reference to the nature of irrational beings [that is, animals — it is not a law of biology], "but because reason, which decrees it, properly belongs to human nature" (CCC #1955).  For example, the Church teaches that artificial contraception is against the natural law, not because it's a rational human intervention rather than an irrational biological process, but because it's contrary to right reason.  It violates the integrity of human nature by divorcing the two naturally united aspects of the essence of the sexual act — the unitive and the procreative — that is, personal intimacy and reproduction.

"The natural law, present in the heart of each man and established by reason, is universal in its precepts and its authority extends to all men" (CCC #1956).  It's not universally obeyed, or even universally admitted, but it is universally binding and authoritative.  ("Authority" means "right," not "might.")

"The natural law is immutable and permanent throughout the variations of history" (CCC#1958) because it is based on God-made essential human nature, which does not change with time or place, rather than man-made cultural developments, which do.

Because man's essence does not change, but his circumstances and situations do, "application of the natural law varies greatly" (CCC #1957).  For instance, capital punishment may be morally necessary in a primitive society but needlessly barbaric in a society with secure laws and prisons; and the moral restrictions on warfare today, with its weapons of mass destruction, must be far stricter than those in the past.

"It provides the necessary basis for the civil law" (CCC #1959), for civil law forbids many acts, such as rape and torture and slavery, because they are morally wrong and harmful to human nature's health and flourishing.  Without a natural law basis for civil law, civil law becomes based on power, whether collective or individual.