The historical background to our citizenship amendment, like so much else, has to do with the Civil War and slavery. (I apologize for going into History Professor mode, and for not knowing how much you already know.)

In the Dred Scott case (1856), the Supreme Court ruled, in essence, that no black was a citizen, and that they had "no rights which a white man was bound to respect" (the words of Chief Justice Roger Taney). After the war, it was vital to establish that all were citizens equally. The Civil Rights Act of 1866 established this for former slaves, but how to settle the question in perpetuity? The way to do this was by the 14th Amendment, arguably one of the most important ever passed:

"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. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws."

Notice that persons not subject to the jusrisdiction of the United States at the time of their birth are not automatically citizens; for example, a child of foreign diplomats is not a citizen, since they are not subject to US law, they are under diplomatic immunity. And it's arguable whether a child of illegal immigrants is a birthright citizen, since the parents themselves are not subject to the jurisdiction of the United States... but would the child be? That's something I haven't looked into and am not going to, right this minute.

29 countries grant birthright citizenship. We're not the only ones, despite what trump might think. (I use the term "think" in the loosest possible sense.) [nomadcapitalist.com]