The case of the United States v. Leon involves the 4th amendment, particularly what is known as the "exclusionary rule."  The question under consideration was whether evidence collected when executing a search warrant issued by a judge had to be excluded from trial if it was found that the judge had given that search warrant based on questionable evidence.  In short, how far can a judge's judgment be called into question when issuing search warrants, and what happens to the evidence involved?

It's a convoluted case from 1984, but it boils down to this:

1. The police were observing a "drug house.'
2. People went in and came out with suspicious bags, including a known drug dealer named Ricardo Del Castillo.
3. When looking into Del Castillo's probation records, they saw that he had listed as an employer a man named Alberto Leon.
4. Leon had been arrested in 1980 on drug charges, and it was suspected that he was involved in the importation of drugs into the country.
5. An informant told police that Leon had lots of drugs in his house.
6. A warrant is prepared by police based on these observations and the informant's assertion.
7. A warrant is signed by State Superior Court Judge.
8. The warrant is executed, and drugs are found.
9. A motion was filed by the defendant to exclude the evidence found because they reasoned that the initial search warrant had been based on flimsy evidence.

The district court ruled to exclude some of the evidence in question because it found the search warrant to be questionable in establishing probable cause, a decision which eventually made its way up to the federal Supreme Court.

The Supreme Court reversed the decision, essentially creating the "good faith" exception in the process.  They found that if the police have presented evidence that was accurate, and a judge issues a warrant based on that evidence, and the police have lawfully executed it, all parties have acted "in good faith."  If the basis for the warrant that the judge has signed is later called into question, evidence seized is still usable in court.  The police cannot be in the position of "second guessing" search warrants, and the practice of having outside parties doing so (especially at trial) risks losing the public's trust in the legal system as obviously guilty individuals are let go because of "technicalities."

That's the importance of this case: it establishes a "good faith" exception in the gathering of evidence when it's based on a legal, but questionable, search warrant.