Marbury v. Madison is significant because it established judicial review. After President John Adams lost his reelection bid to Thomas Jefferson, Adams appointed a number of Federalist judges in the late stages of his presidency, and these judges came to be known as the “midnight judges.” One of this judges, William Marbury, did not have his appointment delivered before Jefferson took office, and Jefferson’s Secretary of State, James Madison, promptly halted the appointment. Marbury sued Madison, arguing that Madison did not have the power to stop delivery of a previous appointment.
The Supreme Court was led by Chief Justice John Marshall at the time, and the Supreme Court cited part of the Judiciary Act of 1789 unconstitutional as part of their 1803 ruling.
On the surface, this did not seem like a very important case, but the precedent of judicial review, or the idea that the judicial branch is the ultimate interpreter of the Constitution, is monumental because it solidifies the judicial branch as being on the same level of power as the executive and legislative branches.
Marshall was a Federalist and a political opponent of Jefferson, and many view this ruling as an assertion of power by Marshall to establish the judicial branch as an entity able to check the power of the other two branches, which it succeeded in doing.