This debate, conducted in the Senate in early 1830, was important because it laid out the arguments for and against states' rights. This was important because the issue of states' rights was what had led to the Nullification Controversy a short time before and it was what would lead to the Civil War.
The major issue between the two Senators was whether the Constitution was a compact between states or between the people of the US. If it was a compact made by the states, then each state had the right to interpret it. If it was made by the people, the federal government had the right to interpret and the states had much less power.
This was an important debate because of the way that it laid out the major arguments that would help lead to the Civil War.