The significance of Marbury v. Madison is that the ruling in that case gave the Supreme Court of the United States the power of judicial review. Judicial review is the power to determine whether a law passed by a legislature (in this case, Congress) is constitutional. In Marbury, the Supreme Court took the power to declare that laws passed by Congress were null and void if they (in the Court’s opinion) violated the Constitution.
Before Marbury, it was not clear which branch (if any) of the federal government could interpret the Constitution. The Constitution clearly stated that laws were invalid if they were not in accordance with the Constitution, but it did not say who got to decide if laws were invalid. This was an important issue because the Constitution would not really have much meaning if Congress (for example) could make any law it wanted to simply by saying that the law was constitutional.
In Marbury, the Supreme Court declared that a law passed by Congress (the Judiciary Act of 1789) was unconstitutional and it therefore said that the law could not be enforced. This was extremely important in our history because it established that the Court could overrule acts of Congress that were unconstitutional. This has had an immense impact on our history because it has allowed the Supreme Court to rule on laws that have had to do with everything from the price of hauling freight on railroads to child labor to abortion. This has made the Supreme Court an important player in our history.
Very simply, John Marshall gave the Supreme Court the power of Judicial Review. Now, the 9 unelected Judges on the Supreme Court had the power to declare a law passed by an elected legislative body either Constitutional or unconstitutional.
This case established the legal rule of judicial review. Before this case, the Supreme Court didn't have much power and this gave them the power to review laws/treaties that the legislative branch wants to pass to see if they are following the constitution.
The Marbury v. Madison of 1803 was important because it was the first Supreme Court case to apply the principle of judicial review, the power of federal courts to void acts of Congress that were in conflict with the Constitution. Please see the following links for even more information.