Something storied is well-known, sometimes even legendary. Your grandmother might love to tell long tales all about her storied past as a Hollywood starlet.
You’re most likely to encounter the adjective storied in a literary context, describing someone or something with a celebrated history. Baseball is an old and familiar sport with a storied past, for example. An earlier meaning was “decorated with scenes from history,” like an illustrated book about the Revolutionary War or the paintings on the wall of a history museum.