I believe that the assertion of the Supreme Court as the sole interpreter of the Constitution becomes the lasting significance of the case. The idea that no other branch except the judicial can determine if actions or laws meet the standard of Constitutionality has become a foundational element of our of nation and our system of jurisprudence. The case firmly established the Supreme Court and the Judicial Branch as one that possesses its own sense of power in relation to the other two branches. In the end, this becomes a vitally important element to American government and society, given the cases it has heard since and the decisions rendered in those cases. These were only made possible through the assertion of the court's power in the Marbury vs. Madison case.
The significance of Marbury v. Madison 1803:
1. It was the first Supreme Court case. Remember the Constitution was effective 1789 and the Congress and the Executive branches were operating. The role of the high court would not be established until it heard its first case.
2. The case established the principle of 'judicial review'. This principle gave the court the power to interpret the meaning of the Constitution. When Chief Justice John Marshall determined that the 1789 Judiciary Act passed by Congress conflicted with the Constitution the court deemed the law 'null and void' (Unconstitutional)
3. Because the principle of judicial review was created as a result of this case the court essentially gave the power to itself, increasing the power of the federal government by enforcing Article VI of the Constitution- the federal government is the supreme law of the land.
4. The power of judicial review has basically shifted the final say on what is and what is not Constitutional in the hands of the Supreme Court. Some critics have argued that the Supreme Court is the most powerful branch of government because its decisions cannot be 'checked and balanced' by the other branches of government. The only branch of government that can overturn a Supreme Court decision is the Supreme Court itself.
When Thomas Jefferson (a Republican) won the election of 1800, John Adams (a Federalist) quickly appointed a number of his own party members to fill key positions as his outgoing action. John Marshall, his Secretary of State, was supposed to fill out papers finalizing these appointments and give them to the people who had been appointed. Their appointments weren't official until they got their papers. Marshall did not get the papers to several of the appointees in time but he assumed that Madison, who would be taking his place in the new administration, would do it for him. Jefferson, seeing an opportunity, told Madison not to give them their papers, essentially making those appointments invalid leaving him with the ability to fill those positions with members of his party, One of those people who did not get his papers was Marbury. Marbury sued Madison and took the case all the way to the Supreme Court in an attempt to force Madison to deliver his paperwork to him as Adams had promised. This case is significant because it established a precedence of judicial review. It also established that Marbury had a right to his commission, even though he didn't get it, and that there was a means by which he could argue his case in the courts. Essentially, this means that the Supreme Court is entitled to review acts of Congress. In this case, however, it was a no-win situation for the court because even if they found in favor of Marbury, Jefferson would not honor the decision and that would lead to animosity between the President and the Supreme Court. The answer they finally came up with was brilliant in that they acknowledged in writing that yes, in fact Marbury deserved his commission, but they could not force Jefferson to acknowledge it. It was Marshall's error that cause him to not get the commission, and the courts would be acting unconstitutionally if they attempted to force Jefferson to honor Adams' unfinished appointments.
Marbury vs. Madison laid the foundation for the process of judicial review. This came about because outgoing President John Adams, following his unsuccessful bid for re-election, placed Federalist judges in newly created positions. Jefferson took office prior to many of these appointments taking place, and so refused the appointments. William Marbury filed a writ of manamus demanding that the appointments be delivered by the Secretary of State, James Madison. The Supreme Court denied this, saying that parts of the Judiciary Act was unconstitutional. This formally set the precedent for judicial review.
I'm not sure how you analyze it, but I can tell you why this was important.
This case was important because it gave the Supreme Court the power of what is called judicial review. This is the power to say that laws made by Congress are unconstitutional. When the Supreme Court does this, it is saying that a particular law passed by Congress is illegal and may not continue to be a law.
The Constitution does not say that the Supreme Court may do this, but in this case, the Court took that power for itself.