This is one of the essential cases in Supreme Court history, for it was the first time U.S. Supreme court had to apply the “judicial review” principle, involving the power of federal courts to avoid acts of Congress in conflict with the Constitution. Thus it makes it a must in the lawyer's background.
It was in 1803 if I am not mistaken when the Supreme Court decided to landmark the case of William Marbury against James Madison, who at the time was a Secretary of State of the United States. The principle of judicial review was confirmed by the Court, and the ability of Supreme Court to limit Congressional power by declaring legislation unconstitutional - into the new nation.
The court ruled that the President (Thomas Jefferson) was wrong when prevented William Marbury from taking office as justice of the peace for Washington Country in the District of Columbia. But, notably, it also ruled, that the court had no jurisdiction in the case and could not force Jefferson and Madison to seat Marbury.
There were also other rules of the court, but I personally find them not that remarkable to write about. If you are deeply interested in the case, you should Google for more information. The case is remarkable for each person who studies law and jurisprudence, that is for sure. But the case is way too long to describe here, as for me. There are loads of papers on the topic, which take more than 3 pages in a row describing each detail of the process.