This was the case that truly gave the Supreme Court their power.
John Adams was a Federalist. He was the president of the USA at one point. However, soon, Jefferson won the presidency. However, Jefferson was an anti-federalist. So Adams was rushing to fill the court with Federalists, by making more spots and filling them with people. However, his presidency ended before some people could get their commission papers. Marbury was one of the people who didn't get their commission paper. He sued the President for that reason, and they went into court. However, the Supreme Court and that time was generally weak and didn't have much power. Jefferson, no matter what, wasn't going to give Marbury his paper. However, the chief justice at that time, John Marshall, knew it was against the law. But he knew the president would just ignore his decision. So instead, what he did, was he stated that one of the powers the Supreme Court had was to declare things unconstitutional. And from there the power of the Supreme Court truly started.