The United States Constitution states: “All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.”
The particular subset of this obvious provision that is sometimes questioned is jus soli, literally meaning, right of the soil.
This is and was a part of English Common Law, which is a good point of reference for any ambiguity, as though there were any ambiguity. It means that if you are born here you get to be a citizen here. A fairly common exception made to jus soli birthright citizenship is for diplomats or similar, people who are also treated to some degree as though they are not actually here at all. So, if a diplomat can commit a felony but not be prosecuted, then they can’t drop a baby and have it be granted citizenship. But otherwise, the interpretation, though fought many times in the courts by nationalists and other asshats, is straightforward.
The reason this is even a thing right now is because the Republicans, under Russian-owned and controlled Donald Trump, are against it, and Trump plans to produce an executive order reversing jus soli for brown people. What’s next? Removing citizenship from anyone who’s home land is not an actual state? (Like Puerto Rico?)