Grey market is when you buy a product in one country/region that was intended for purchase in a different country/region. For example, if you buy a VCR that was intended for use in the UK here in the US, or a tractor that was intended for sale in Japan. Manufacturer's often have to tailor their products for a certain market. For example, power supplies for a VCR, as well as the video signalling, are different here than in the UK. On tractors, sometimes the direction and speed of the PTO are different than they are in the US. I'm sure there are a lot of other differences, but these are just examples. One other that comes to mind might be the language of the owner/operator manual.
Aside from obvious incompatibilities like PTO speed/direction or voltage requirements, there is often no real problem with using the item. Many manufacturers, if you read the warranty closely, will void the warranty for grey market stuff. This is especially true for electronics. Depending on the manufacturer, it can sometimes be difficult to get parts/service for a grey market item. Some companies make a single model with a few variations for each region, others have completely different products for each region. It just depends.
As for how to determine what is grey, if you receive the literature that should have come with it, it will often point this out. Some manufacturer's that are frequent "victims" of this practice list models/serial numbers that are considered grey (I think Kubota does this on their web site). If all else fails, you could try contacting the US office for the company and see if they can help (if they don't have a US office/contact of some kind, this may be a good indication the item is grey).
Kevin