Those laws which regulate (1) the structure and administration of the government, (2) the conduct of the government in its relations with its citizens, (3) the responsibilities of government employees and (4) the relationships with foreign governments.
Good examples are tax law, criminal law and especially constitutional law.
It can be distinguished from private law, which regulates the private conduct between individuals, without direct involvement of the government.
Private law and public law can overlap. For example, an unsolicited punch in the nose would constitute a crime for which the government would prosecute under criminal law but for which there would also be a private legal action possible by the injured party under tort law, which is private law (although governments can be held responsible under tort law).