What is the administration of justice? There is a need for the administration of justice when people or companies do not agree and are not able to solve a conflict themselves.
The judge will then decide which party is right according to the law. In criminal cases, the judge will (mainly) investigate the question whether the facts in the accusation can be proved and, if they can, which punishment should be imposed. Criminal cases are part of criminal law.
Besides the area of criminal law there are also civil law and administrative law. An example of a civil case is when a couple wants to know which of them the children are going to live with after their divorced. An example of a case of administrative law is a foundation or an association that does not agree with a government decision to stop subsidizing them.
A judge is impartial and adheres to the rules of the law: the legal system. One of the reasons for the administration of justice is to prevent people from taking the law in their own hands. Because we live in a constitutional state, everyone should adhere to the rules of the law. This goes for the citizen, but also for the government and for the judge as well.