Satin was a fabric known for having an exceptionally soft and luxurious feel.
When the USS Enterprise-E was transported to 2063, the ship became infested with Borg and Captain Jean-Luc Picard escaped with Lily Sloane into a holoprogram of the Dixon Hill series. As he called up the program on the computer, he suggested "Perhaps something in satin?", confusing her. The reference became clear, however, as the program dressed her shimmering satin evening gown. (Star Trek: First Contact)
In 2373, Q, in an attempt to woo Captain Kathryn Janeway, placed a bed in her quarters, complete with red heart-shaped pillows and satin bedsheets. Janeway, however, was not amused and ordered him to remove it. (VOY: "The Q and the Grey")