Naturalization is also, in biology, the process when foreign or cultivated plants have spread into the wild, where they multiply by natural regeneration.
Naturalization is mentioned in the Constitution proper. Congress is given the power to prescribe a uniform rule of naturalization, which was administered by state courts. There was some confusion about which courts could naturalize; the final ruling was that it could be done by any "court of record having common-law jurisdiction and a clerk (prothonotary) and seal."
The Constitution also mentions "natural born citizen". The first naturalization Act (drafted by Thomas Jefferson) used the phrases "natural born" and "native born" interchangeably. To be "naturalized" therefore means to become as if "natural born" -- i.e. a citizen.
Naturalization is also mentioned in the Fourteenth Amendment. Before that Amendment, only white persons could be citizens of the United States. The Amendment states that "all persons born or naturalized in the United States and subject to the jurisdiction thereof shall be citizens of the United States and of the State in which they reside." Therefore, all persons born in the U.S. are citizens regardless of race.
There is an interesting loophole here in that the Constitution does not madate race-neutral naturalization. Up until 1954, the Naturalization Acts written by Congress still allowed only white persons to become naturalized as citizens (except for two years in the 1870's which the Supreme Court declared to be a mistake.)
Note also that the Amendment is ambiguous on the issue of singular or plural United States. In the early days the phrase "United States" was used as a singular or a plural according to the meaning. After the Civil War, it was generally always a singular. The Amendment does not say "its jurisdiction" or "their jurisdiction" but "the jurisdiction thereof".