It usually means a life full of interesting or significant events and experiences that could be told as stories.
Well, 'a storied life' suggests that the person has had a rich and diverse life journey with many tales to share. Maybe it involves achievements, challenges overcome, or unique adventures that make their life stand out.
Basically, when we say 'a storied life', it indicates that the individual's life has been filled with memorable moments, possibly having gone through various ups and downs, and having accumulated a collection of remarkable stories worth telling.