A tooth sharpener is a small hand-held device with a cylindrical grinder at one end, used by Ferengi to sharpen their teeth. The grinder rotates at high speeds and is applied to the edges of a tooth in order to sharpen it. Although Klingons also have relatively sharp teeth, Worf had never seen one before.
Rom owned a latinum-plated tooth sharpener as a child and the device held a strong sentimental value for him. His son, Nog, held a similar attachment to his own tooth-sharpener and it was among the personal items that he auctioned off prior to his departure for Starfleet Academy where it was purchased by Worf. (DS9: "Little Green Men")
Later that year, Worf's quarters were burglarized. Among the items stolen was his tooth sharpener. This incident compelled him to request to live on the USS Defiant. (DS9: "Bar Association")
Quark was forced to use a wooden "chewstick" instead of a tooth-sharpener, which he blamed on not being Ishka's favorite son. (DS9: "Family Business", "Little Green Men")