When the Mexican-American War ended, the United States received the Mexican Cession which included all of California, Nevada and Utah, and parts of Arizona, New Mexico, Colorado, and Wyoming. With this huge land acquisition, the issue of slavery in the new territories was raised. This led directly to the Compromise of 1850. This compromise deepened the division between the North and the South. First, California would be admitted to the Union as a free state, which upset the South. Two new territories would be established, Utah and New Mexico. These territories would be open to slavery through popular sovereignty, that is, the people of the territories would decide the issue of slavery. This upset the people in the North because so much territory could now have slavery. The slave trade was banned in the District of Columbia which upset the South because they saw this as a first step towards abolishing slavery. There would be a new, strict, fugitive slave law which upset the North because now by law they had to assist in returning slaves to their owners. These tensions created by the Compromise of 1850, which was passed because of the results of the Mexican-American War, helped create the conditions for the Civil War.
The previous posts were quite accurate. The acquisition of more land helped to perpetuate the slavery question. Prior to the war, the Missouri Compromise had somewhat tabled the issue in terms of establishing an equal balance of slave and free states. Yet, the compromise failed to account for the dynamic nature of both the issue and the nation. The issue was too intense with feelings too passionately experienced on both side to simply be "tabled" with a compromise. The nation was too dynamic with industrial energy as well as expansionistic desires to remain intact. With the war and its eventual acquisition of more land, the question as to what status those states would become ended up reigniting the passion behind the debate. The proposal for popular sovereignty to decide the issue again ignited intense discussion and debate about the nature of slavery, leading into the Civil War.
In my opinion, the importance of the Mexican-American War was that it destroyed the compromises between North and South that had previously been established. By doing so, it reopened the arguments over the extension of slavery. This caused the North and South to grow further apart and finally split.
Before 1846, the Missouri Compromise had more or less solved the issue of the expansion of slavery. But now, the war threatened to bring more land into the United States. Significantly, all this land would be in the South. This made the North very suspicious of the war and of the motives behind it.
Once the land was taken from Mexico, a debate arose over whether it would be free or slave. The process of debate led to such things as the Compromise of 1850. This debate, as I said, reopened the suspicions that the two regions had of each other and forced them to argue once again over the extension of slavery.