William Marbury was appointed as a justice of the peace by Pres. John Adams and his appointment was approved by the Senate, but the actual commission confirming his appointment was not delivered before Pres. Adams left office and Pres. Thomas Jefferson named a new Secretary of State, James Madison. Sec. Madison refused to deliver the commission due to basic differences in political philosophy between Marbury and the new administration. Marbury responded by suing the government, stating that Madison was required to deliver the commission based on Section 13 of the Judiciary Act of 1787.
In his ruling, Chief Justice Marshall agreed that Marbury had the right to receive the commission. However, he found that the Judiciary Act of 1787 gave the Supreme Court authority that was not delegated to it in the Constitution.
The original jurisdiction of the Supreme Court (when the Court acts as a trial court) was limited to cases “affecting ambassadors, other public ministers and consuls, and those in which a state is a party.” Because Marbury was in none of those categories, and there was no mention of the authority to issue writs of mandamus at the trial level, the Court refused to assume jurisdiction over his case, despite the fact that Congress granted the Court such power is Section 13 of the Judiciary Act of 1789.
This was the first time that a judge ruled that a law could not be enacted if it didn't follow the guidelines and restrictions set out by the Constitution. Marshall was also establishing that the Supreme Court had the power to make interpretations of laws to determine if those laws were within the authority delegated to the branches of the government by the Constitution.