If something is a characteristic of someone or something, it is a feature you would expect. A characteristic of classical-style architecture is large stone columns. A characteristic of poodles is their pom-pom like tails.
A characteristic feature needn't just be a something physically apparent, it can describe a type of personality or atmosphere as well, as in: "The characteristic of all funeral homes is their gloomy air." As their spelling and meaning implies, there is a close link between the words characteristic and character, meaning the essential nature of a thing, and in fact both words come from the ancient Greek kharackter, meaning a "symbol or imprint on the soul."