This crisis began when the Congress passed the "Tariff of Abominations" in 1828. A tariff would hurt the South, which relied on trade, and help the North, because it would protect Northern industry from foreign competition.
The South was very unhappy and, in 1832, South Carolina said it would not obey the law. It claimed that states were free to ignore any law that was not (in their opinion) constitutional. If this were allowed to stand, the Union would be in danger because each state could basically ignore the federal government whenever it wanted to.
Pres. Jackson resolved the crisis in two ways. He prepared to use military force against South Carolina if they did not back down. At the same time, however, he got Congress to ease up a bit on the tariff so that the South would not feel so abused.