Law is a set of norms, or a collection of them, established and promulgated as public knowledge so that people can study them, internalize them, figure out what they require, use them to settle disputes with others, and protect themselves against abuses of private or public power. It also requires that legal institutions be independent, accountable, and transparent in their processes.
This is a complex concept with many dimensions. The more general signification of the word, derived from the Greek, refers to laws that regulate action in the realms of nature and non-human animals: man, as a creature endowed with reason and free will, is commanded to obey these laws (natural law). This notion, however, does not quite capture the fundamental role of law, which is to ensure that individuals are treated fairly by and have a way to challenge the actions of powerful entities that exert authority over them.
This is a very challenging task for the societal institutions that are tasked with it. Inevitably, people disagree and conflicts arise; for example, if two people claim the same piece of property the law is used to determine who owns it. The law allows these conflicts to be settled peacefully without violent confrontations, and it enables individuals to trust that their rights will be respected by the state and that public officials, including the police, will carry out their duties properly. The Rule of Law thus provides a crucial safety net against a dangerous world.