Demount tyres are new tyres that were fitted to new vehicles but have done no mileage worth talking about. Usually this happens when vehicles are shipped from the factory with one particular brand on the rims but the brand chosen by the vehicle manufacturer changes by the time the vehicle reaches the destination country!
The reason you should care is that you can get a new premium branded tyre (just with no labels) at a fraction of the price!
This is a tyre that has been on a set alloy wheels in a showroom but when sold the tyres need to be changed to correspond with the vehicle they are being fitted to.