The issue was whether or not the court had to approve appointments made in the last days of John Adams presidency, as Marbury and the others claimed. The court ruled in favor of Madison, and, in so doing, established for itself the principal of judicial review.
Marbury vs. Madison was a Supreme Court case in 1803. The plaintiffs were William Marbury, William Harper, Robert R. Hooe, Dennis Ramsay. The defendant was James Madison (who was Secretary of State at the time). Madison won, and no one voted against him. The Court determined that Marbury and the others did not have a right to their commission, because they were not confirmed.
"It is, emphatically, the province [within court's power] and duty of the judicial department [the courts] to say what the law is." This dramatic and often quoted statement was made by Chief Justice John Marshall inMarbury v. Madison (1803).- See first link
The case was important in establishing the concept of Supreme Court Judicial Review. We now view the Constitution as a living document. Chief Justice John Marshall declared: “A Law repugnant to the Constitution is void.” As a result, the Constitution is now interpreted by the Court.