Each of the 50 States of the United States has its own Constitution. A State's Constitution plays a vital role in setting up the structure of the State Government and in defining the rights and expectations that citizens of the State possess. Although often overlooked and rarely taught, State Constitutions can be a very important source of rights.
An example is the privacy rights people may or may not have in their garbage. The U.S. Supreme Court has ruled that people do not have any federally protected right to privacy in their garbage (California v. Greenwood, 486 U.S. 35 (1988). However, individual State Supreme Courts have found that their State Constitutions afford more rights than the U.S. Constitution and thus have prohibited state law enforcement officers from searching an individual's garbage (see e.g. State v. Goss, 150 N.H. 46 (2003), finding a reasonable expectation of privacy in one's garbage that was protected by the New Hampshire State Constitution). The U.S. Supreme Court, in the Greenwood decision, recognized that individual states might find more privacy rights in their own Constitutions than exist in the U.S. Constitution.
A State's Constitution is the highest source of law provided by that State. However, it is not the final arbiter of rights afforded to citizens of that State. Article VI, Clause 2 of the U.S. Constitution states:
This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.
In other words, State Constitutions are void to the extent that they conflict with the U.S. Constitution, U.S. Laws, or Treaties to which the United States is a signatory.