The court system is the system of the law which is used for the purpose of justice.
It is the system in which determines the punishment of a criminal for example, it will determine how long a sentence for a particular crime should last for, the worse the crime, the longer the prison sentence.
The court system has developed over 1000 years, therefore there may still be some older laws in place which are less relevant to today's modern society.
Each crime is handled differently within the court system, for example, less serious criminal cases start off in the magistrates court. The crimes in which are much more serious are sent to the crown court. After the cases have been to the crown court (if needed) they will then be sent to the court of appeal or even the supreme courts which deal with the extremely serious cases and criminals.
http://www.judiciary.gov.uk/about-the-judiciary/the-justice-system/court-structure/