The Four Paws Quick-Fit Cat Muzzle box says that the muzzle covers your cat’s eyes, which creates a calming effect. Jay Leno talked about the Four Paws Quick-Fit Cat Muzzle on his show (at about the 2 minute mark on the video) and didn't seem to agree.

The Quick-Fit Cat Muzzle might come in handy when you have to transport your pet to the vet and you don’t want him to see the other animals in the room. It could also function as part of a Halloween costume.