See? I told you it was confusing.
Nullification is the idea that if the federal government passes a law that one or more states don’t like the states can reject the law.
In the case of the Nullification Crisis it was the Tariff of 1828, which was extremely protectionist. Farmers in the South liked low tariffs because they had to import almost everything. Merchants in New England liked high tariffs to keep foreign competitors out. The Tariff of 1828 was intolerably high as part of a gambit to force New England and John Quincy Adams to split. It didn’t work.
A current analog would be the bill that passed a couple weeks ago to allow Americans to sue foreign leaders. The Republicans wanted it for some reason, Obama explained repeatedly that it sets an atrocious precedent. They forced it through anyway, then blamed Obama for not mentioning how bad it is for foreign relations. So imagine that, but ending with Mitch McConnell threatening to go to South Carolina and declare independence because of how bad the bill is.