According to the Bible of the Christian religion, Adam and Eve were the first humans on Earth that were created in the image of God. They would later be cast from the Garden of Eden after succumbing to temptation of the Devil and disobeying God's law. (TOS: "The Apple") According to myth, all humans thereafter were said to be descended from Adam and Eve.
In 2254, when Christopher Pike was abducted by the Talosians, he was placed in a position to begin a new population of humans on Talos IV, where he was allowed to choose his mate. His options were limited to Vina, "Number One" and J.M. Colt.
After their subsequent released, Colt later inquired to Pike who his choice for "Eve" would have been -- a question Pike found inappropriate. Intrigued, Dr. Boyce inquired, "Eve as in Adam?", to which Pike replied, "As in all ships' doctors are dirty old men." (TOS: "The Cage")
Spock kept an image of the 20th century art piece Adam and Eve in his quarters aboard the USS Enterprise-A during the late 23rd century. The expulsion of Adam and Eve from paradise, was to him, a representation that reminded him that all things must end. (Star Trek VI: The Undiscovered Country)