The right to privacy is the right to be let alone, in the absence of some "reasonable" public interest in a person's activities, like those of celebrities or participants in newsworthy events. Invasion of the right to privacy can be the basis for a lawsuit for damages against the person or entity violating the right.
The right to privacy is not mentioned in the Constitution, but the Supreme Court has interpreted several of the amendments as creating this right. One of the amendments is the Fourth Amendment, which stops the police and other government agents from searching us or our property without "probable cause" to believe that we have committed a crime. Other amendments protect our freedom to make certain decisions about our bodies and our private lives without interference from the government. The due process clause of the 14th amendment generally only protects privacy of family, marriage, motherhood, procreation, and child rearing.