an excellent explanation by Rythmdvl. not only did his response post before mine, it was much more clear. i would only add the following:
the reason the Judiciary Act of 1789 was unconstitutional is that expanded the Supreme Court’s original jurisdiction. “Original jurisdiction” is a court’s ability to hear a case that hasn’t been appealed up through the system (essentially, the Supreme Court is like the trial court). the Judiciary Act of 1789 said that 1) you can ask the Supreme Court to issue a writ of mandamus (which, for our purposes, forces the government to do something), and 2) when you want to do that, you don’t have to start with the District Courts and then mess around for years in the appellate courts; you can just start your case in the Supreme Court.
but the Supreme Court said, “Thanks, Congress, for giving us this power, but the Constitution of the United States says we can’t have original jurisdiction over these mandamus cases.” the problem, according to the Supreme Court, was that the Supreme Court’s original jurisdiction was defined and limited by the Consitution. since the Supreme Court’s original jurisdiction had been spelled out in the the Constitution (which is the Supreme Law of the Land), then the only way to change the Court’s original jurisdiction was to amend the Constitution.
what is so striking about this decision is, as Hugh seems to have grasped, that this thing came out of (pretty much) thin air. there is nothing about “judicial review” in the Constitution, or any of our statutes or treaties. further, it doesn’t appear in american common law prior to this point (in Europe, when a legislature passed a law, it was de facto constitutional–the courts there seemed to rely on a presumption that the legislature could tell at least as well as the courts what laws conflicted with superior laws). but the decision was framed in such a way, that the Supreme Court was able to pass on ruling in a case that would have damaged the Court’s credibility/legitimacy if it had ruled, and to actually increase the Court’s power by passing. as an example of the disdain the Executive branch had for the Supreme Court and the Supreme Court’s absolute lack of power prior to this decision, the Supreme Court had ordered Madison to appear before them and explain why he hadn’t delivered the commissions, and Madison ignored the order. he didn’t even argue his case to the Supreme Court.
so when the decision came out, Congress and the President weren’t going to complain because they got what they wanted (Marbury didn’t get his commission). and with the advent of judicial review, the Court went from being the least powerful branch of government to arguably the most powerful.
it’s probably also worth noting that there wasn’t an immediate uproar because the Court didn’t strike down any more laws as unconstitutional for a long, long time after this decision. i like to think of them as sort of sitting on this power and hoping noone notices, although it was probably just judicial restraint. ho hum.