A (largely historical) British automotive term referring to the type of car known to Americans as a convertible and to the French (and Europe in general) as a cabriolet (although all of these terms may carry a more specific feel as to the exact style, but this has varied over time). In other words, a car with a cloth top which folds down but does not remove from the car, giving an automobile that serves as an open-top car in good weather yet can be covered easily should more inclement weather show up, even on the road (though generally one has to be stopped to deploy the top. The term does not refer to removable hardtop cars, whether or not the hardtop can be stowed inside the car.
Generally used in the expression drophead coupe, referring to a car with two doors and a soft top. You'll generally find cars produced by elegant British marques like Alvis, Aston Martin, Bentley, Lagonda, Rolls Royce and the like referred to as Drophead Coupes, as well as European cars of similar stature when referred to by British writers. Frequently, four-door cars were referred to as Cabriolets, though not always. Soft-top cars of the modern era tend to be called convertibles or cabriolets in British usage, the term drophead being reserved for classic automobiles and their rare modern counterparts.