One can basically become a citizen of a country in one of two ways: by virtue of birth, or birthright, in which case he is known as a natural-born citizen; or by being granted citizenship after birth, in which case he is known as a naturalized citizen.
The U.S. is one of the few countries in the world which grants birthright citizenship automatically to individuals born on U.S. soil (under most circumstances), known as the jus soli concept (jus soli is Latin for “right of the soil”). There are ways for one to be a birthright citizen other than being born on U.S. soil, namely, to be born abroad if both parents are U.S. citizens or, in some circumstances, if one parent is a U.S. citizen. The State Department summarizes the law here.
We can have a legitimate debate about the merits of the jus soli concept, and also whether this practice is actually mandated by the constitution: there is a constitutional argument that a child born of illegal immigrants on U.S. soil need not automatically be granted U.S. citizenship.
What Donald Trump is really talking about is ending the jus soli principle, at least in some cases. He should clarify his language, for even though no one (as far as we are aware) is talking about ending birthright citizenship as such, our politicians and pundits are muddying the waters—often deliberately. It would be useful for presidential candidates to state whether they oppose jus soli citizenship in all cases, in some cases (such as when the mother or both parents are in the U.S. illegally), or not at all. Trump’s immigration policy paper mentions “the children of illegal immigrants” in passing, but does not fully explain his position.
For an example of the obfuscation, see James Taranto eviscerate a misleading tweet, which claimed that Sen. Ted Cruz (R-Tex.) is a hypocrite for attacking “birthright” citizenship even though he is a “birthright” citizen. Wrong: Cruz is indeed a birthright citizen, because his birth abroad to a U.S. citizen mother fulfilled the requirements of birthright citizenship, but he is clearly opposing granting birthright citizenship to people born in the U.S. to illegal immigrants. Cruz is opposing at least one application of the jus soli principle, and he is not a jus soli citizen—much less one born to illegal immigrants—which of course is not hypocritical at all. Donald Trump is also a birthright citizen, but he is also not a hypocrite for opposing a certain type of birthright citizenship.
In defense of the tweeter, the article to which he linked does cite Ted Cruz’s opposition to “birthright citizenship” multiple times, including in the headline, and it appears that Cruz used those two words in the radio interview that was the subject of the article. However, Cruz was talking about birthright citizenship when the parents are in the U.S. illegally, which is a special case that provides necessary context to any discussion of the subject—and which the headline, from CBS Dallas, also deliberately, or negligently, failed to represent.
Jeb Bush recently referred to “a noble concept, which is birthright citizenship” in attacking Donald Trump’s calls to end it. Presumably he was thinking of jus soli as the noble concept. Are politicians and the media avoiding the proper, precise Latin term for simplicity, or because “birthright citizenship” is a euphemism that is hard to argue against?