Velvet was a type of fabric.
In 2268, Spock was manipulated into singing the song Maiden Wine by the Platonians which had the second line, "Be watchful of young men in their velvet prime." (TOS: "Plato's Stepchildren")
In 2373, an insane Silaran Prin referred to "the velvet cloak of darkness". (DS9: "The Darkness and the Light")
Acrylic paint on black velvet was a 20th century Human art form. In 2373, Quark auctioned off a painting of a matador done in this fashion. Morn won. (DS9: "In the Cards")