WHAT DOES the "UNITED STATES" MEAN?

LEGALLY, United States is the sovereign that the states of the Union created to represent them on a national level. So legally, United States is the FEDERAL GOVERNMENT, which is sovereign over District of Columbia and territories.That can be clear from the Article XI of the US Constitution, since the Judicial power of the United States CLEARLY means there the jurisdiction of the federal gov't, barring a Citizen of one State to sue another State in federal court:

"[Article XI] (Amendment 11 - Suits Against States)
The Judicial power of the United States shall not be construed to extend to any suit in law or equity, commenced or prosecuted against one of the United States by Citizens of another State, or by Citizens or Subjects of any Foreign State."

But TERRITORIALLY, it's not so clear. It could be the territory of all the 50 States, OR the territory over which the US government has exclusive jurisdiction - which would be District of Columbia and territories. I tend to think that it is the later, since the combined territory of the 50 states would be called United States of America, because it'd make no sense if the territory of the 50 states would be called the same as territory over which the federal gov't has jurisdiction.

But it also should be noted, that the United States gov't is a FOREIGN CORPORATION with respect to a State, so its statutes and codes do NOT apply in States of the Union, UNLESS the US Constitution specifically authorizes such codes. 

I.e. powers that has not been specifically delegated by the States to the federal gov't via the Constitution, DO NOT EXIST. Well, except when you're a 14th Amendment citizen; then you're subject to federal law, no matter where in the world you are.