We need courts because their work is to apply the law of the country, settle disputes and punish the guilty.
They are also responsible for upholding the rights of citizens and seeing that no one, including the government violates them..
We need a court system to
a) deal with criminal matters from shoplifting to murder
b) uphold the rights of the people being tried. Rights such as habeas corpus and the infamous Miranda rights.
c) carry out the awesome duty of declaring laws either constitutional or unconstitutional. This power is called judicial review, and it was kind of taken by the Supreme Court in the Case of Marbury v. Madison during which the chief justice John Marshall dismissed the case on the grounds that Marbury's case was based on an unconstitutional law. This is where the supreme court was given the power to decide the constitutionality of things like gay rights and Obamacare.
the court is the place to settle a lawsuit ~~