When adams was appointed president, he appointed Marbury as Judge. The commissions that were supposed to be sent him were prepared.
The issue was that thomas Jefferson stopped Madison from sending the commision for appointing Marbury as the judge.
Marbury argued he was entitled to the writ because his commision was already created. He argued that the supreme court had the power to give the writ.
One side( Marbury)
Madison is the secretary of state didn't deliver the commissions.
The court said Madison was right about not getting the commision, but disagreed with him saying the court had the power to give the writ. Because the court couldn't issue the writ Marbury couldn't get his commission.
They created a judicial review where they can stop the other branches from doing something over the constitution. because of this case all the branches have equal power.