When the judiciary act was founded, It opening new spots for more judges. Adams tried to fill these spots, but there were still many commissions not delivered. So when the Jefferson was inaugurated and Hamilton became secretary of state, they were supposed to deliver the rest, but refused to. One of these was William Marbury's.
I, William Marbury, sue James Madison to force him deliver my commison
John Marshall knew if the court awarded Marbury a writ of mandamus, the Jeffersonians would ignore it, weakening the courts. But if they denied it, it my seem like they acted out of fear
Marshall finally came to a decision. He said that Jefferson and Hamilton should hand out the rest of the letters, but the court didn't have the power to enforce it, Deming the Judiciary act unconstitutional.
This would be the first act to be Unconstitutional, and gave equal power to the Judicial power. This power was the power to reveiw.