Let us break down what justice is; justice is behaviour that is just or fair. So the justice system is the system that enforces the law which involves apprehending the accused, prosecuting the accused, defending the accused, sentencing and punishing the guilty. The justice system makes sure that every citizen is heard for and is helped according to what has happened to them.
The criminal justice system today
When a person commits a crime there are different levels of punishment and decision making if a person has committed a minor crime like speeding, littering, shoplifting, prostitution, vandalism being drunk, possession of drugs etc. They are either given tickets and left off with a warning or spend 1 night in jail some of the cases like vandalism will require them to do community service and others like drug possession can land them into jail for a few years. Then there are bigger crimes that are more serious like murder, manslaughter, rape, Assault with the intention of killing, Arson etc. These offences come with harsh punishment like life imprisonment, many years in prison sometimes if a person has murdered someone multiple times they are known as serial killers and will be taken into death penalty.
Ways they caught suspected criminals in the middle ages

In the middle ages there was no police force but instead of the police force the villagers would suspect something had happened they would scream at the top of their voices and everyone who heard them would have to