this seller lists the camera as "Import Model 1 Yr Parts & 30 Day Labor Warranty via Seller"
"Warranty via seller": this is where the biggest difference with an official product is: the seller's own repair team of technicians fixes your camera if it has any problem.
This means they'll open the camera (or lens) themselves, voiding any warranty in the country where the equipment was originally sold, any unsuccessful repair attempt could cause further damages in the camera (a real case I've encountered personally). For these reasons I see grey market as being tinted with black because not all is made clear and / or transparent.
If repair can't be made, the seller may tell you it's not really a problem, will not recognize or admit the issue, etc..., or if the seller is reputable and serious, will send your equipment at his/her own cost to an official Pentax / Canon / Nikon / Fuji / etc repair center, in the country of origin of the camera. You then usually have to wait several weeks to few months until the camera is repaired.
The above is my experience from interaction with online sellers, discussions with photographers who bought grey / parallel import photographic equipment and my own experience from having once bought from such a store (not online but walk-in store). Asking the good questions to the store clerk revealed many interesting facts.
Now why the business is good for such sellers and advantageous for customers? Because cameras, besides the cases thoroughly detailed by @MichaelClark above, are mostly, if not always, genuine when purchased from a reputable seller, and nowadays cameras are reliable so warranty rarely needs to be activated. You'll find far more satisfied grey market customers than unhappy ones.
So buying grey from a reputed seller is a risk, which could be approximately quantified as the probability that a camera needs a fix within the warranty period (not taking into account how intensely the camera is used, whether or not all possible features of the camera are used, etc...), a low risk but a real one. It's worth considering the purchase of used but official equipment (also from a reputable seller / user).