It is important to understand that when people read your resume or peruse your LinkedIn profile, they are formulating an opinion about you. That opinion is based solely on the limited facts that they have, and those facts clearly don't tell the person everything. But your resume and LinkedIn profile do tell a story, and the reader's time is limited. As such, these assets can either put you in contention for a great job or can immediately take you out of the running without an opportunity to fight for yourself.
While you can't change history (and it is critical you are truthful about the facts), you shape perception either by the decisions you make into the future or by how you tell the story about your past. You want to be able to tell the right story for the jobs that can best unlock your potential.
Here are some of the storylines potential employers perceive, how they arrive at them, and what you can do to ensure you're telling the correct ones.