So he had his Secretary of State (James Madison) NOT deliver the commissions. William Marbury was ticked at that, so he sued Madison, saying that he HAD to deliver it.

Well, Jefferson didn't want the new people.

So right as he left office, he got the Judiciary Act signed to let him appoint a bunch of new judges/justices of the peace. BUT they weren't official without their commissions.

Adams wanted more control of the court.

So you know the basics...

Hence, why it is called Marbury V. Madison...

" Though Marbury was entitled to his commission, the Court was unable to grant it because Section 13 of the Judiciary Act of 1789 conflicted with Article III Section 2 of the U.S. Constitution and was therefore null and void. " 

So what does that mean?

It means:

The Judiciary Act was unconstitutional, and therefore everything it did can't be allowed

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a.k.a. - the commission isn't valid because the act that created the commission was illegal​

So the court just declared something to be unconstitutional - that had never happened before...

We call this judicial review

Judicial review means that the Supreme Court has the power to declare a law or executive action unconstitutional.

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This case was when this power was established. ​