Xanadu was a city in Mongolia.
It was the summer capital of Kublai Khan, grandson of Genghis Khan. In the 13th century, the Venetian explorer-merchant Marco Polo visited the Khan there. After the fall of the Mongolian Empire, Xanadu lay in ruins, and eventually came to be thought nothing more than a myth.
In 2152 on the Torothan homeworld, when Jonathan Archer used the name of the city in a geography game, Trip Tucker disputed his use of it, claiming Xanadu was "fictional". Archer replied "That doesn't matter." (ENT: "Desert Crossing")
Xanadu is in fact not fictional: its ruins were located in the 20th century, but the association of the name with insubstantial, exotic legend persists.
In a scene deleted from "Fight or Flight", Travis Mayweather also referenced Xanadu in a game of geography with Archer. The two actually used the same locations as Tucker and Archer did in "Desert Crossing", but in this scene, it was Mayweather who used Xanadu and Archer who disputed its legitimacy.