Trailer queen is a (somewhat disparaging) term used by classic car enthusiasts to refer to vehicles that don't get to classic car shows under their own steam but rather arrive on a trailer (or more often, in a closed trailer, so no speck of dust can mar the paintwork). Cars entered in most competitions do have to be drivable and are driven from the trailer to their assigned place of display, but that's all the distance such cars ever travel, with the addition of slow drivepasts and parades.
Vehicles are brought to shows on a trailer for two reasons; firstly, simply because the owner doesn't want to put many miles on the car that could cause wear and damage, and doesn't want to risk it in heavy traffic, and secondly because the standards of perfection in many concours d'elegance competitions mean that any trace of road grime would be unacceptable.
That fact rankles with many car nuts, because the essence of a car is as a means of transportation, and because the acceptance of trailering cars to shows and competitions means that those who wish to actually enjoy using their vehicles for transport have little chance of winning competitions with them. Many also feel that for all of a trailer queen's beautiful cosmetic restoration and paintwork, the hard work of restoring the car mechanically to a state of mechanical reliability often has not been done. Originally, many concours d'elegance prohibited trailering or gave automatic penalties to it so that trailered cars would not have an unfair advantage over driven cars. This practice has largely ceased, and few winners are driven to the show anymore.
To somewhat compensate, many contests now feature classes for driven cars only, but these do tend to feel like consolation prizes, second rate sideshows to the main event.
The flip side, of course, is the fact that the show champions brought on trailers to the show are in absolutely immaculate condition. Many, in fact, are in better shape than the day they left the factory.