Public law is the branch of law that governs the behavior of people and is enforced by the state. Public law is distinct from private law, which focuses only on people's relationships with each other. Public law relates to a person's state-mandated obligations to behave in a certain manner.
In the US, laws are all divided into two categories: public and private laws. Private laws are enforced by citizens only. For example, if a person breaches a contract or commits a tort, an act that causes harm to another person, those violations are violations of private law. When a private law is violated, the victim who is harmed by the violation can sue in civil court. The government does not involve itself in enforcing private laws, other than the level of involvement associated with providing a court system to hear the cases and enforce penalties.
All public laws must be enforced by some aspect of government interference or intrusion. In this sense, they are distinct from private laws in which one individual brings a lawsuit against another. Private laws are enforced by litigation, while public laws are enforced by law enforcement.
Public laws include Constitutional law, criminal law, and administrative law. The Constitution grants rights to individuals, but also vests them with a responsibility not to do harm to others. If a person violates the Constitutional prohibitions against deprivation of life, liberty, or the pursuit of happiness, then the court can impose penalties.
Criminal laws are also public laws. Criminal laws are laws that are made in order to create an ordered society. If a person violates a criminal law, although their victim is another individual, that person still violates the public law of society.
Laws imposed by administrative agencies are also public laws. For example, in the US, the Environmental Protection Agency (EPA) places limitations upon a person's right to dispose of hazardous waste materials. This is a public law, enforced by the EPA, because improper disposal of waste can lead to problems for society at large.
Public laws are normally enforced by government agents or officials. For example, if a person commits a crime, he or she can be prosecuted by a federal or state prosecutor. The victim of the crime need not press charges, or even want the crime to be prosecuted, but the government officials can still punish the criminal for the violation of public law.