It changed how the Fourth Amendment was interpreted.
Prior to Katz a physical intrusion into some protected space was required before the Fourth Amendment was violated. In Katz the majority ruled that the Fourth Amendment protects people, not places. They ruled that Mr. Katz had a "reasonable expectation of privacy" inside an enclosed phone booth; and that the Fourth Amendment had been violated since the police did not have a search warrant to listen in and record his conversation.
The citation is Katz v. United States, 389 US 347 (1967).