In Mapp v. Ohio (1961), the Supreme Court ruled that evidence obtained in violation of the Fourth Amendment's protection against unreasonable searches and seizures can't be used as evidence in state courts (this was already not allowed in federal courts). The case arose from a 1957 search of the apartment of Dollree Mapp in Cleveland, who was suspected of harboring a bombing suspect. In searching Mapp's apartment, the police found pornographic books, which they used to arrest her. Mapp was found guilty in state court and appealed to the Supreme Court on the basis of the idea that the police had no probable cause to expect that she was in possession of pornography.
The case affected citizens of the United States by providing them with additional protections. If the police violate one's civil liberties in conducting an illegal search or seizure, the evidence the police obtain cannot be used in court. If a defendant feels that evidence was obtained illegally, the defense counsel can use a "motion to suppress" to have that evidence excluded from trial.
The Supreme Court case of Mapp v. Ohio (decided in 1961) affected US citizens (and everyone who lives in the United States) by saying that state law enforcement officers could not use evidence obtained through illegal searches and seizures in court. In technical terms, it applied the exclusionary rule to the states.
The 4th Amendment says that government officials cannot conduct searches or seizures without warrants. However, the amendment does not spell out what happens if they do conduct such searches. The exclusionary rule (made up by the Supreme Court) says that the evidence found in such searches cannot be used against a defendant in court. This is the punishment for violating the 4th Amendment—you do not get to use the evidence you have found.
However, the 4th Amendment only applied to the national government. Most police forces are controlled by the various states (local police forces are included in this). This meant that state and local police were not subject to the exclusionary rule. This changed with Mapp. This case applied the exclusionary rule to the states. It affected US citizens by protecting them from having evidence used against them in court if that evidence was gained through an illegal search or seizure.