Article 3 of the Constitution created the supreme Court and gave it 'the judicial power of the United States'.
The USC awarded itself the power of judicial review of the legislature by striking down an act of Congress in Marbury vs. Madison (1803)
The president has no control over the decisions of justices after nominating them, so they do not always do what the president wants. For example, in Trump vs Vance (2020) Neil Gorusch and Brett Kavanaugh ruled against the interests of Trump
Notable examples of USSC cases that have had a large impact on culture are Brown v Topeka (1954) which ended segregation and Roe v Wade (1973) which legalised abortion.