A natural-born citizen refers to someone was was a U.S. citizen at birth, and did not need to go through a naturalization proceeding later in life.
Political Office Requirement
The phrase "natural-born citizen" appears in the U.S. Constitution. In order to become the President or Vice President of the United States, a person must be a natural-born citizen. This "Natural-Born Citizen Clause" is located in Section 1 of Article 2 of the United States Constitution.
The constitution does not expressly define “natural born” nor has the Supreme Court ever ruled precisely upon its meaning. One can be a citizen while not being a "natural born" citizen if, for example, that person gained citizenship through the process of naturalization.
Under the 14th Amendment's Naturalization Clause and the Supreme Court case of United States v. Wong Kim Ark, 169 US. 649, anyone born on U.S. soil and subject to its jurisdiction is a natural born citizen, regardless of parental citizenship. This type of citizenship is referred to as birthright citizenship.
There is some debate over whether or not one may also be a natural born citizen if, despite a birth on foreign soil, U.S. citizenship immediately passes from the person's parents.
Today, 8 U.S.C. § 1101 defines naturalization as “conferring of nationality of a state upon a person after birth, by any means whatsoever.” In contrast, § 1401 lists eight categories of peoples who are "nationals and citizens of the United States at birth," including those born in the United States and subject to its jurisdiction, as well as children of one or more U.S. citizens abroad as long as the parent(s) meet certain requirements. This means that foreign-born citizens falling under a provision in 1401 are, by statutory definition, not naturalized. The term "natural born" is not used, however.
For more on natural-born citizens, see this Georgetown University Law Center Immigration and Nationality Law Review article, this Harvard Law Review article, and this Fordham Law Review article.