Table linen was a term referring to cloth items used during one's meal, such as tablecloths and napkins.
In 2371, Miles O'Brien declined an invitation from Benjamin Sisko to dine with Admiral Drazman, citing "full dress uniform, fine table linens, a different fork for every course" (i.e. the formality of the meal) as his reasons for not wanting to be there. (DS9: "Past Tense, Part I")
Later that year, while forced to share quarters with his brother, Quark accused Rom of stealing table linens, among other items, from Quark's to furnish his living space. (DS9: "Prophet Motive")