In the preamble, the phrase “establish justice, insure domestic tranquility” means

This phrase is part of the U.S. Constitution's preamble that states the following: We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.

In overall, the Preamble is a brief statement that sets the Constitution's fundamental purposes and guiding principles. The Founding Fathers wrote the phrase “establish Justice, insure domestic Tranquility” to establish one of the reasons that the document was made: to create a system of laws for internal peace.