The word "privacy" is nowhere to be found in either the Bill of Rights or the rest of the U.S. Constitution.
Even without being directly stated, the idea of the right to privacy was put forth by Justice Louis Brandeis in his dissent voiced in the Olmstead v. U.S. case. Brandeis believed that individuals had a "right to be let alone," which could be inferred through the Fourth Amendment's protection against "unreasonable searches and seizures." Brandeis reasoned that the Founding Fathers expected individuals to have secure possession over papers in a home without intrusion from the authorities. Even through Brandeis's opinion didn't garner a majority, his view on privacy would inspire future cases on privacy rights and influence a firm answer on the right to privacy in the case Griswold v. Connecticut.
In 1961, Estelle Griswold opened a birth control clinic which gave counseling and birth control to married couples. The counseling and devices violated Conneticut's "Comstock Law," which prohibited the use of any birth control aimed to prevent conception. The Supreme Court struck down the law and recognized for the first time that there was a "right to privacy" in the Constitution. Even though it's not explicitly stated, Justice William Douglas reasoned in his majority opinion that there were "penumbras" in the Constitution where the right to privacy was implicit. Douglas listed protections against the self-incrimination clause in the Fifth Amendment as well as unreasonable searches and seizures in the Fourth Amendment as examples of the "penumbras" in the Constitution to justify a right to privacy.
The right to privacy would become a powerful tool for future justices in protecting certain rights, such as abortion in Roe v. Wade. In 1969, Norma McCorvey sought an abortion, but Texas law only allowed for abortion in the instance of rape or incest. McCorvey eventually petitioned to the Supreme Court for relief. The court ruled in favor of "Roe" and stated that abortion was a protected right under the right to privacy.
The court then adopted a trimester framework in determining whether states could regulate an abortion. In the first trimester, states could not impose restrictions on abortion. In the second trimester, states could administer regulations but could not restrict the procedure. In the third trimester, states could restrict abortion in order to protect the life of the fetus. Thus, through the right of privacy that isn't explicit stated, the right to an abortion was determined to be guaranteed by the Constitution. Roe v. Wade demonstrates the importance of the right to privacy and how it has been used to ensure certain rights.