Cinderella was a classic folk tale from Earth. It was the story of a young girl who found true love and happiness after a period of neglect and abuse at the hands of her evil stepmother and stepsisters.
In 2267, James T. Kirk told Yeoman Teresa Ross (who was dressed in a ball gown and wanted to change her clothes) to "turn in (her) glass slippers; the ball is over." (TOS: "The Squire of Gothos")
Pavel Chekov – who believed the story to be a Russian epic – referenced this tale in 2293, while snapping at Crewman Dax (who he thought might be familiar with the story) "If the shoe fits, wear it!" while informing him that the magnetic boots used to board Kronos One were discovered in his locker. At the time, Chekov did not realize that as a Megazoid, Dax' webbed feet were unable to fit into standard boots. (Star Trek VI: The Undiscovered Country)
In the script for "Star Trek: The Undiscovered Country", Chekov believed Cinderella to be a Romulan epic.