Learning professionals know this saying well. When they design training programs, they know to incorporate stories, multiple forms of media, and interactivity to engage the learner and reinforce their learning.
Stories, we have long known, are powerful tools for teaching. Homer's Illiad, American Indian's stories, Aesop's Fables, heck, even our own family history, have morals and lessons within. Some of these stories have great impact because we connect with them.
If a job seeker's mission is to educate, then their stories are the vehicle to make that happen. Stories provide demonstration of abilities, convey the traits and characteristics that define you, thus contain a moral. This moral is either important to the future employer or not. Your job is to make sure the stories you tell are in sync with future employers by researching them thoroughly.
Kathy Hansen's mission is to educate on the importance of story sharing. A Storied Carrier is full of evidence that story telling is a very strong component of life.
If a job seeker is to consider part of their search as a training session, how have they engaged the "learner"? What forms of media have they incorporated in the presentation of themselves? How have they connected with the learner (aka future employer, networking contact, etc)? How have they ensured their message will be remembered?
Stories are not just important in job search. They are also key to success on the job as well. Maintain a portfolio of your work, collect testimonials from customers, keep co-worker emails that express gratitude or praise. It isn't enough to just do your job anymore. You need proof that you're making a difference in the organization. It is the responsibility of everyone working to prove their ROI (return on investment) to their employers.