Why was the supreme court decision in marbury v madison of 1803 important?

Marbury v. Madison was important  because it asserted the Supreme Court's right of judicial review -- the ability to declare a law or executive action unconstitutional.

More detail:

Judicial review refers to the courts' ability to review any law to see if it violates any existing law or any statute of a state constitution or the US Constitution.  On the federal level, Marbury v. Madison (1803) is considered the landmark case for the Supreme Court asserting its authority of judicial review, to strike down a law as unconstitutional.It was sort of a roundabout way in which the principle of judicial review was asserted by the Supreme Court in the case of Marbury v. Madison. William Marbury had been appointed Justice of the Peace for the District of Columbia by outgoing president John Adams -- one of a number of such last-minute appointments made by Adams.  When Thomas Jefferson came into office as president, he directed his Secretary of State, James Madison, not to deliver many of the commission papers for appointees such as Marbury.  Marbury petitioned the Supreme Court directly to hear his case, as a provision of the Judiciary Act of 1789 had made possible.  The Court said that particular provision of the Judiciary Act was in conflict with Article III of the Constitution, and so they could not issue a specific ruling in Marbury's case (which they believe he should have won).  Nevertheless, in making their statement about the case, the Court established the principle of judicial review.

It was the first U.S. Supreme Court case to apply the principle of "judicial review".