Actually, it's not clear at all. The amendment does not assume that "born or naturalized" implies "subject to the jurisdiction thereof."
The question, of course, is what does "subject to the jurisdiction of," mean?
What it has always meant: that US law applies to you while you are on US soil.
Unlike Native Americans prior to 1924, for example, who were subject to the jurisdiction of their tribe or nation on their reservation, since the reservation was - in a technical legal sense - not US soil for personal jurisdiction purposes.
And unlike diplomatic personnel recognized by the US and their immediate family members.
“what does “subject to the jurisdiction of,” mean?”
Well, it appears clear beyond doubt that the Republican Congress, immediately following the Civil War/War Between the States, intended the 14th Amendment to mean that anyone who could waddle across our southwestern border and drop their child in an American hospital, at our expense—well, then that child is an American and also a serviceable anchor for scores of his/her relatives.
And there should be no quibbling or argument, particularly over whether the 13th, 14th and 15th amendments were specifically passed to protect freed slaves and their children (with hazy memories of Africa and certainly not anxious to return, Liberia to one side) not subject to the jurisdiction of their former tribes, whereas conventional wisdom and experience is that Mexicans remain Mexicans, in spirit and practice, while availing themselves of American largesse. No, that’s all nativist hatred, not argument.
However, “the right of the people to keep and bear arms” could mean just about anything you know, so let’s litigate its meaning until free men/gun nuts simply give up and turn over their rifles and handguns to the proper authorities and the notion of a “free republic” is as strange to our grandchildren as the notion of “American citizenship” will be to our children.