ReasoningThe holding was derived from several reasons.
The court first contemplated whether Marbury has a right to the commission that he wants delivered to him. The Marshall Court established that, since his commission is for a legal position, and not for a political one, the Executive branch does not have the power to terminate it without violating his vested right to the position. As his right has indeed been violated, the court decided that the laws of the United States and judicial system need to provide him a solution it is the duty of the judicial branch to do so. The court also states that since an officer has indeed infringed up on the right of an individual, a mandamus is a valid remedy to consider.
However, the Marshall Court found that the Act on which this request is based on, Section 13 of the Judiciary Act of 1789, is in conflict with Article 3, Section 2 of the US Constitution. Section 13 increased the Supreme Courts power, giving it the right to issue writs of mandamus in appellate and original cases, whereas the Constitution stated that the Supreme Court has original jurisdiction only for cases affected ministers, ambassadors, and consuls. Section 13 does indeed justify the granting of a writ, but Article3 Section 2 does not, as Marbury does not belong to any of the groups mentioned