A brooch is a type of jewelery, typically a decorative ornament that was worn near the wearers neck or hair.
Ambassador Lwaxana Troi had her latinum hair brooch, which had been in her family for thirty-six generations, stolen while in Quark's during her visit to Deep Space 9 in 2369. When Quark was approached about it, he referred to the sign above the door that stated that "we are not responsible for the loss of items." This was totally unacceptable to Ambassador Troi, who demanded "I want this room sealed and everyone in it strip-searched, until you find my brooch." Thereafter, Odo got involved in the investigation, and after a series of deductions was able to determine that the thief was a Dopterian patron. (DS9: "The Forsaken")
After being accidently transported to 21st century San Francisco, Jadzia Dax stated that she had been robbed, and that they had gotten everything except her brooch, which was the term she used to describe her Starfleet communicator. (DS9: "Past Tense, Part I")
Quark read a passage from Odo's romance novel which described how the female character moved her hands to the brooch at her throat, which she proceeded to unclasp, allowing her cloak to fall from her shoulders. (DS9: "The Ascent")