"North American Union" refers to a plan - or just a desire - to join the U.S., Canada, and Mexico into one country or under one government of some kind.
Like immigration, a vast array of establishment hacks have tried to mislead about this topic, such as by playing word games. They've pretended that if there are no concrete plans to create such an entity then it's just a fantasy. That's despite the fact that steps that the establishment is taking are making such a union more likely and establishment sources have outright proposed such a union. For the first, see the posts below and note also that around 14% of Mexico's working-age population already lives in the U.S. For the second, see this, this, this, this, and many others.
And, it's despite the existence of George W Bush's secretive Security and Prosperity Partnership, which was designed to "harmonize" regulations between the three countries. Liberal-leaning establishment hacks who would never take the Bush administration's word for anything were more than willing to take the Bush administration's word that the SPP wasn't a precursor to a NAU.
See also this and, related to the NAU, the NAFTA Superhighway. The latter is something that the same hacks said didn't exist despite the fact that it already exists in Texas as the TransTexasCorridor; there are or were plans to extend it to other states, and a Canadian government map and province governor both referred to it by that name.