Essentially, national law is the rules and laws that govern a particular country. These can include things like constitutions, treaties and laws that are enacted by the government of a country. They are different from international law, which relates to the obligations of countries that are signed up to treaties and conventions.
In some cases, it is difficult to tell whether something is national or international law. For example, the European Union’s directives require EU countries to achieve certain results but leave them free to decide how to do so. This means that if a country does not implement the directives by a specific date, then the European Commission may initiate infringement proceedings against it.
In general, however, the national and international rules are separate from one another. Nations are often divided into parts for administrative convenience, so that they can have state laws to deal with regional matters, and then local law for units like cities and towns. These are usually based on the national law, although it is possible that some local rules might be derived from international law, depending on the situation. National law is binding on its own territory, but international law is not. For example, a Dutch court might decide that a treaty such as the European Convention on Human Rights is part of national law if it has been ratified by the Netherlands. This would be because the Treaty operates automatically, as a legal rule of the country, within the legal system of the Netherlands, and not as a separate body of legislation.