Nasal Expanders or dilators prevent nostril collapse and allow more air into the nose. Generally it come in 2 main types, those that open the nostrils from the outside and those that dilate the nostril from the inside.

(A) The external dilator often consists of a stiff strip that is applied to the outside surface of the nose with adhesive, much like a stiffened Band-Aid. It works by pulling the nostrils open, easing breathing through your nose and reducing snoring.
(B) The internal dilator, which is inserted into the nostrils and remains in place during sleep.

These will work for a very small percentage of snorers, as it is often mistaken that snoring is due to the blockage of the nostrils, rather than the airway. As far as I know, nobody snores because their nostrils are flapping around in the breeze, so these devices don't work the way it should to stop the snoring.

Now the reason this only works for such a small percentage of people is that the amount of difference you can make to the inhalation vacuum by widening your nostrils is insignificant. Maybe, if you were just barely snoring (ie your inhalation vacuum was causing your airway to just barely collapse enough for you to snore the tiniest little bit) and you widened your nostrils as much as you could, your snoring might stop.