The term "establish Justice" in the preamble of the Constitution means to "begin fairness for all." There are reasons why this statement was added into the preamble of the Constitution. The preamble explains the reasons why the U.S. government was formed a certain way.
The preamble to the United States Constitution is an introductory statement outlining the Constitution's purposes both fundamentally and guiding. The revolution against England involved many important aspects, which were all important to the American citizens. The U.S. government has a legal system that is expected to make fair decisions regarding citizens' problems. The need developed for a judicial system that could handle any disputes arising between states or a dispute arising from people whom resided in different states. This ensured that all persons would be treated fairly and equally and guaranteed that their rights would be respected by others. It ensured that no individual nor entity had was superior to civil and criminal statutes. Adding this phrase into the preamble of the Constitution helped the American citizens feel secure in knowing that they would have justice under the new constitution. This phrase was meant to establish a fair court system. The court system referred to is the one which protects citizens' rights in the court of law.