When it's a tourte mute. These are typically used to change the sound characteristics of string instruments. Rather than making them quieter, it seems to take away between 10-20% of their resonance. As a result the instrument sounds darker, and it makes it harder for the produced sound to travel longer distances. This means your neighbours will probably have an easier time, but the people sitting in front of you might not notice a difference.
If you are searching for something to colour your playing, this is it. If you're looking for something to make your instrument substantially quieter, you'd be far better off buying a practice mute instead.