Puerto Rico is a territory located in the Caribbean sea, this territory is under the control of the U.S. government. This means, Puerto Rico is not an independent country by definition but in some aspects is part of the United States.
This includes the fact people who are born in Puerto Rico are citizens of the United States, and therefore they do not require a passport or permission to travel; in the same way, people living in the U.S. can travel to Puerto Rico. This relationship between Puerto Rico and the U.S. is the result of the Treaty of Paris signed in 1898 in which the U.S. acquired this territory. According to this the country that is a territory of the U.S. and does not require a passport for travel is Puerto Rico.
