The administration of President Andrew Jackson is notable because it represents a huge increase in the power of the Executive Branch. Jackson abandoned many of the past moderate customs of the presidential office and used his power and influence in overt and powerful ways.
One way he did this immediately upon taking office became known as the spoils system. In his run for the presidency, Jackson had made grand promises to his supporters. When he became president, they lined up to collect. Jackson quickly removed hundreds of established public officials and civil servants from their posts and replaced them with his supporters. This became a precedent that, although there have been reforms put in place, still exists in some form to this day.
Jackson exercised his power even further during the nullification crisis. When the government of South Carolina declared recent federal tariffs to be unconstitutional, Jackson asked Congress for the authority to use military force to enforce them. While the matter was soon resolved without bloodshed, never before had a president been given the authority to use his power as commander in chief against American citizens.
Jackson also held many racist beliefs. He felt that Native Americans had no right to land ownership. As such, his administration ignored the Supreme Court decision of Worcester v. Georgia and forcibly removed the Cherokee people from their ancestral land. He also violated the First Amendment when he ordered the post office not to deliver abolitionist materials. Although he saw himself as a "man of the people," Jackson limited this to white people only.
Jackson also exerted extreme power when he withdrew all federal funds from the Second Bank of the United States. He disagreed with the bank's lack of funding for territorial expansion as well as its political influence. He saw the bank as an institution of the elite. As a populist, Jackson felt that the bank did not serve his political agenda.
As you can see from all these examples, the Jackson administration represents a massive expansion of the reach of the Executive Branch driven by the political and personal agendas of the president.