Answer:
They interpret the laws set forth by the Legislative Branch of the government. In America they would be the Supreme High Court of Justice. They are NOT a standard courtroom with a judge and jury. The duty of the Judicial branch is to interpret CONSTITUTIONAL laws. Matters that conflict or may pose a problem with the Constitution are interpreted and dealth with accordingly.
Eg. A man could not go to the Supreme Court of Justice demanding for them to hear his case if he had been implicated in a murder. But a man could go to the Supreme Court of Justice on the basis that in some rally, his freedom of assembly had been subdued. This is part of the constitution therefore it is the duty of the Judicial branch to examine it.