Marble was a type of rock often used for ornate constructs, such as statues and buildings. On Earth marble was commonly found in the region of Italy.
Kathryn Janeway once asked of the hologram of Leonardo da Vinci if he knew "nothing of the politics of Florence, the cutting of marble or mathematics?" (VOY: "Concerning Flight")
In 1893, after Joe Falling Hawk won the pot in a hand of poker on a bluff, Frederick La Rouque observed that his was "A poker face carved in marble." (TNG: "Time's Arrow")
Tom Paris explained to B'Elanna Torres that their honeymoon would be "Six days and seven nights in the historic Graystone Hotel in beautiful downtown Chicago, circa 1928," adding, "Wait till you see it/ Crystal chandeliers, [and] wall-to-wall Italian marble." (VOY: "Course: Oblivion")
In 2063, during Geordi La Forge's encounter with his childhood hero, Zefram Cochrane, he explained how there was a statue of Cochrane located in almost the exact place Cochrane was presently standing. La Forge described that statue as being "marble, about twenty meters tall and you're looking up at the sky. Your hand sort of reaching to the future." (Star Trek: First Contact)
When Data inquired to his creator, Noonien Soong, in 2367 as to why he created him, Soong referenced to a saying attributed to Michelangelo, stating, "That the sculptures he made were already there before he started, hidden in the marble. All he needed to do was remove the unneeded bits." (TNG: "Brothers")
The Kohl hostages of the Clown, referred to themselves as "his canvas, his blocks of marble. With us, he practices his ghastly art." (VOY: "The Thaw")