Jackson did a number of important things, but since the question asks for just one, I will argue that his policy of Indian removal was the most important of all of his actions. Jackson had been a longstanding advocate of westward expansion, and his policy of removing Cherokee, Creek, Choctaw, Seminole and Chickasaw peoples from lands in the southeast to make way for southern farmers represented an important moment in the development of a cotton-producing South.
Jackson's policy had dreadful ramifications for Indian peoples, especially the Cherokee, who died en masse on the Trail of Tears, the name given to their removal to Indian Territory in the west. Because most of the people who moved into the fertile lands vacated by Indians grew cotton, it also led to the expansion of slavery, and the beginning of a massive slave trade from the Upper South. It also had important political implications, as Jackson had patently refused to enforce the Supreme Court's decision in Worcester v. Georgia, which had stipulated that the Indian Removal Act was unconstitutional. Indian removal underscores the reality that Jacksonian democracy and the politics of the common man were both based upon the oppression and the denial of political rights to blacks and Native Americans.