According to the Bible of the Jewish and Christian religion, the Garden of Eden was the habitat created by God for the first Humans, Adam and Eve. They would later be cast from the Garden of Eden after succumbing to temptation of the Devil and disobeying God's law. In common parlance, Eden became a symbolic word for paradise.
Soon after, Pavel Chekov inaccurately believed that the Garden of Eden was located "just outside Moscow." He claimed that it was "a very nice place" and that "it must've made Adam and Eve very sad to leave." (TOS: "The Apple")
In 2268, James T. Kirk metaphorically called the planet Neural a Garden of Eden. He also referred to introducing flintlocks to the Neural natives as introducing serpents to the Garden of Eden. (TOS: "A Private Little War")
In 2293, Spock kept a piece of 20th century Earth art called "Adam and Eve Expelled from Paradise" in his quarters. The painting depicted a scene of Adam and Eve being cast out of the Garden of Eden. For Spock the painting was a reminder that "all things end." (Star Trek VI: The Undiscovered Country)
In 2364, while the USS Enterprise-D visited planet Edo, Lieutenant Natasha Yar described the planet as "like an Eden". (TNG: "Justice") Later in the year, Luisa Kim, a terraformer on Velara III, referred to herself as a "Gardener of Edens". (TNG: "Home Soil")