One important thing the nullification ordinance says is that in 1828 and again in 1832 Congress passed tariffs that were supposed to collect revenue from foreign imports, but in reality had a different aim, namely the:
...protection of domestic manufactures and the giving of bounties to classes and individuals engaged in particular employments, at the expense and to the injury and oppression of other classes and individuals...
The nullifiers meant that the tariffs passed by Congress were intended to protect industry by placing duties on manufactured goods imported from other countries. This meant that Americans would be more likely to purchase American manufactured goods, which were produced almost exclusively in the Northeast, and would be cheaper than foreign goods. This was considered bad for Southern planters, mostly because it had a tendency to raise prices on the goods they purchased.
A second point raised in the Ordinance was that by passing the tariffs, Congress had:
exceeded its just powers under the constitution, which confers on it no authority to afford such protection, and bath violated the true meaning and intent of the constitution, which provides for equality in imposing the burdens of taxation upon the several States and portions of the confederacy...
Here, they argued that Congress was required by the Constitution to distribute the burden of taxation equally, and that the burdens of protective tariffs were borne (if indirectly) disproportionately by the Southern states. So in passing a law so clearly benefiting the people of one region over another, they had violated the Constitution.
A third point, and the one with the most historical significance, was that in light of the alleged abuses of the tariffs, and of their supposed violation of the Constitution, South Carolina would "nullify" it, or simply refuse to allow it to be enforced within its borders:
[The tariffs] ...are null, void, and no law, nor binding upon this State, its officers or citizens; and all promises, contracts, and obligations, made or entered into, or to be made or entered into, with purpose to secure the duties imposed by said acts, and all judicial proceedings which shall be hereafter had in affirmance thereof, are and shall be held utterly null and void.
They went on to say that attempts to enforce the tariffs by force on the part of the federal government would lead South Carolinians to dissolve "their political connection with the people of other States." This threat got to the heart of the issue--South Carolina was denying the ability of the federal government to pass legislation like the tariffs, and they were asserting the right, which had been earlier explained by Vice President John C. Calhoun, to leave the Union if their right to do so was not respected. This began the Nullification Crisis of 1832-33.