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(Thomas Gainsborough. The Painter's Daughters, Margaret and Mary, Chasing Butterfly. Source)
What is a Law? Why do we have Sanctions (or punishments and rewards)?
I don't have the time or the expertise to provide you with a complete explanation of Laws and Sanctions. Please refer to some real philosophers, among others the whole Treatise on Law by Saint Thomas Aquinas [Ia-IIae, q. 90 et al.], and Thonnard). In the meantime, here is my best attempt at a quick primer.
Right from the start, we have to realize that Laws and Sanctions are a bit like "crutches" for the two "legs" of human action: the reason and the will. If your reason is somehow not able to show you clearly what you should do, laws are supposed to support it. In the same way, if your will is not fully capable of making you do your duty, sanctions are supposed to support it. (We say "supposed" because Law and Sanctions can fail. For example, a human law can be unjust, or a sanction poorly enforced or inappropriate, etc.)
We are all more or less aware of this intrinsic insufficiency of Laws and Sanctions. Suppose for example that you are driving in the residential area of a brand-new town, in a brand-new country which hasn't had time yet to enact a Traffic Regulation Act. There might not even be a law forcing you to drive slowly through a residential area, but you will think that driving fast is not a good idea, that "it just makes sense" to avoid speeding. You won't need big traffic signs ordering you to drive slowly.
In the same way, after your reason has shown you that speeding in a residential area is bad, your will probably will make you slow down, even though there are no speeding fines or policemen in that country yet. You won't need to be threatened by sanctions to act well.
This is because, in a limited way, your two "legs" (your reason and your will) are "strong enough" to make you act well. As you probably know, "virtue" comes from a word meaning "strength" or "force", and your reason and will are being strengthened by the virtues of Prudence or "Goalance" and Justice.
If we were all perfectly prudent and just, as soon as we were born, we wouldn't need Laws and Sanctions.
Let's take a simple example of a law: "Thou shalt not stick a fork in the electrical outlet!" Why do mothers of young children "enact" such laws? Because the reason of a young child is not normally capable of generating what is technically known as a "prudential poly-syllogism". Let's look at an informal example of such a beast:
Men are made for happiness, so they have to act in a way that will make them attain this goal (happiness), or at least get them closer to it. If you cease to live, apparently you cannot be happy, so normally we should try to avoid death.
Now, bringing a metallic object (such as an eating implement called a "fork") into contact with a terminal of an electrical outlet carrying the electromagnetic sine-wave of 120V at 60Hz has many possible outcomes. If the terminal that is touched is the Ground or Neutral, no observable effects will occur. If the terminal is the actual Hot one, then the outcome will depend on the actual circuit established and its ohmic resistance.
If, for example, two prongs of the fork simultaneously touch the Neutral and Hot terminals, a very short circuit of low-ohmic resistance should be established, rapidly exceeding the current-carrying capacity of the fuse or breaker normally in series with this outlet. Often a large spark will occur, along with a partial melting of the fork, and nothing else.
If, on the other hand, only the Hot terminal is touched, and no dielectric substance is interposed between the fork and the person holding it, the circuit established could pass through the body of the person, and exit the body where it contacts a low-voltaic potential and high current-carrying capacity object (such as a wet floor). In such circumstances, a current above 0.10 amperes could put the human heart into a state of fibrillation, stopping blood circulation and rapidly causing infarction of encephalic tissue, leading to death.
Therefore, for very young children, Thou shalt not stick a fork in the electrical outlet.
As you can imagine, this kind of inference takes some skill (and remember it is just an informal summary of a real prudential poly-syllogism). But young children are able to understand and remember only the conclusion of this syllogism! Equipped with this conclusion, with this "crutch" for their reason, they can know how to act in such circumstances!
As I've said, I'm giving you a simplified explanation. There are two other aspects of a law which are implicit in this example, and which complicate things a bit. First of all, the mother teaches this law to her child. How could the child's reason be perfected by this knowledge, if it's never transmitted to him? That is why laws need to be "promulgated", i.e. the citizens need to be notified of it. (For certain laws, like the Natural Law, the promulgation is "automatic" because this Law is "written in our hearts".)
The second implicit aspect is the whole problem of "who makes the law". For a mother and her baby, the answer is obvious. For a whole country, it's "whoever is in charge of the Common Good", but after that things can get more complicated. Still, it's a good start to remember the general definition of a law as "the conclusion of a prudential poly-syllogism, promulgated by the leader for the Common Good".
Let's continue with our young child who is immensely attracted to electrical outlets. Providing him with a "crutch" for his reason (a law) might not be sufficent to make him behave. You also have to make that child want to obey the law.
Typically, the mother will do this by artificially modifying the effect of the bad behavior, in order to bring this effect "closer" to the child's will, and also to make this effect far less severe.
In our example, the mother will reduce the "causal distance" by warning the child very sternly that he will get "lots and lots of smack-bottom" if he goes anywhere near a plug with a fork. There is no longer a long chain of events that needs to occur, and there is no longer an uncertainty of the outcome. "Fork near plug" now equals "mucho, mucho pain" for this child. Not only that, but (despite what the child might think), the severity of the outcome has been greatly reduced, from death by electrocution to very temporary, highly localized, and non-threatening pain.
Of course, a mother can often achieve this same result by just talking louder and lowering her voice, but I'm assuming that this first recourse hasn't worked with this child. (I'm not advocating child-beating, but just taking an extreme case to make a point).
Notice also that the "type of causal distance" can vary immensely. For example, it can be "social distance", i.e. the bad behavior hurts somebody else (like a surgeon who botches an operation), or "probability distance", i.e. the bad behavior has a relatively small chance of causing serious harm (like a teenager driving while drunk), or "spiritual distance", i.e. the bad behavior doesn't cause visible, bodily damage, even though it causes great non-physical harm (like a man treating a woman like an object), etc.
This overly-brief introduction to the topic of laws and sanctions is not enough to guide you through life, so don't stop reading good Philosophy books (even though you might not currently see the rationale behind this conclusion of a prudential poly-syllogism!).
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