I assume that you are asking about the case of Katz v. United States, which was decided in 1967. The basic conclusion of this case was that wiretaps on public telephones are searches that are subject to the 4th Amendment. Therefore, such wiretaps can only be placed if the police have a warrant to do so.
In Katz, the issue was whether the police could place a wiretap on a public telephone without getting a warrant. To that point, this had been legal. The public telephone is not a person, or a person’s house, papers, or effects. Those are the things that are protected according to the 4th Amendment. Since the public phone is not any of these, it was not protected by that amendment.
In this case, though, the Court moved away from this logic. It held that the 4th Amendment applied to people and not to things. That is, it held that a person has the right not to be searched without a warrant and that right goes along with them as they move around. When a person uses a public phone, they have the right to expect that no one is listening in on their conversation. Therefore, their conversation is protected by the 4th Amendment.
This was the major conclusion made by the Court in this case.