The nullification controversy happened in the late 1820s and early 1830s. This was a controversy over whether states could choose to ignore a law that they felt was unconstitutional.
In 1828, the Congress imposed a tariff on imports to the US. Many Southern states, and South Carolina in particular, believed that this law was unconstitutional. Therefore, South Carolina said that it would not obey the law. This was controversial because it was essentially a step towards secession. It was a state denying that the national government had supreme authority in the country.
The nullification controversy was important because it was a step that worsened the north-south conflicts that eventually led to the Civil War.