This is a British idiom related to the way an upper class person speaks. It refers to having a deep tone and a refined and somewhat drawling articulation of words. It can also mean desirable, as in "I got a plummy job at the London Stock Exchange"

It's actually a mis-translation, being taught to you as "authentic" English. : / I've only found it on Chinese websites. Do you mean wrinkly skin, after being in the water? Then we say "wrinkled as a prune". We could say "pruney" but it's a little uncommon. We never use "plummy" for this situation, because to us a plum is a fresh, round juicy fruit. We use "plum(my)" to describe pleasant and desirable things.

Interesting ... I cannot recall ever hearing the word "plummy" used by a Canadian or American English speaker. Thanks to Jura's answer, I now know that it's a British English term. However, Canadians and Americans do use a similar term to describe something that is great or extraordinary, such as: The mayor gave his brother a plum job with the city government (also means an easy, great job, perhaps a job that the brother did not deserve or may not have been qualified to do.