Throughout the Star Trek Universe, these were used everywhere. From Engineering to the Captains Ready Room. They came in all different sizes and colours and were mainly used for set dressing, but also as part of the story line.
Here is my example of one.
Came originally from IAW, and verified genuine from the one and only, Penny Juday, Art Department Coordinator via email!!!! She was able to offer me great insight into the production of these props, and also the certain 'tells' applicable to genuine articles. This one is silk moulded on both sides, one side is Gold, the other Silver.
Here is a pic of the same style being used on board the Enterprise-E in First Contact in the left hand corner.