In Marbury v Madison, the USSC asserted its power to review acts of Congress. The outcome gave the SC power to invalidate whatever it determined as a conflict with the Constitution. Thereby establishing the courts power to declare acts of Congress unconstitutional. The SC under John Marshall emphasized that the Constitution is the supreme law of the land and that the SC is the arbiter and final authority of the Constitution. The result of this ruling set the standard that exists till this day.
Actually it asserted its obligation to review acts of Congress. It's a subtle but important difference. The court is simply to determine whether a law is constitutional, not to decide whether it's consitutional. It has an obligation to determine correctly, but that doesn't mean that its determinations are automatically correct.
The SC under John Marshall emphasized that...the SC is the arbiter and final authority of the Constitution.
He did not say that SCOTUS is the final authority. What he did say was this: "...a law repugnant to the constitution is void, and that courts, as well as other departments, are bound by that instrument."
Clearly, according to him, the courts must conform to the law, not the other way around.