A wig or toupée is an artificial piece of hair, most often worn for fashion or traditional reasons.
At one time, it was fashionable for Betazoid women to wear elaborate wigs that caged small animals. The practice, which was cruel to the animals, was stopped when one (unknown) woman stood up against it. (TNG: "Half a Life")
While trying to come up with character sketches for possible stories, Jake Sisko once watched a Bolian from an the upper level of Deep Space 9's Promenade, and speculated that he was wearing a toupée in order to impress a Dabo girl. (DS9: "The Muse")