Andrew Jackson led a very eventful and influential presidency. His chief domestic policies included the elimination of the national bank, the balancing of the federal debt, the assertion of the executive power during the nullification crisis and the removal of the removal of American Indian tribes from their native lands.
Whitehouse.gov describes the battle over the Bank of the United States as one of Jackson's greatest political victories. The Bank of the United States was a private corporation that acted as a state-sponsored monopoly. Jackson was opposed to the perceived elitism it supported. He felt the bank trespassed the rights of the states and gave undue benefit to the mercantile class of the northern states. Andrew Jackson vetoed a bill to recharter the bank four years early, effectively killing it.
Jackson also played a part in expanding the role of the American president. When South Carolina passed an ordinance of nullification against certain federal tariffs, Jackson stepped in and threatened to send in federal troops to enforce the law.
Biography.com notes that one of the most controversial of Jackson's domestic policies was his stance regarding Native Americans. Jackson negotiated treaties that resulted in forced migration, including the infamous Trail of Tears, a relocation that resulted in the death of 2,000 to 6,000 Cherokee Indians.