Show that you're going to love what you do
I came across a video on LinkedIn that had gone completely viral - a woman named Page Kemna created a jingle to convince a prospective employer to interview her.
When you see it, you'll know why it went viral - it's absolutely amazing. She's one of these people more than just regularly talented at music; she's fluent in music. She looks like she's fooling around and having fun, but sounds better than the last professional musician you've heard.
Someone should hire her for something. It's an incredible marketing idea, perfectly executed. That being said, my reaction (and my wife's, who was in HR) was the same: "Wow, what an amazingly gifted singer. She should definitely be in music." That might be why her LinkedIn profile still says: "Resume went viral, but still open to opportunities."
The natural reaction is to think that she should be either a professional singer or an independent jingle writer. And I bet she could leverage the virality of that post to create an entire successful career in either of these two areas.
More than anything else, employers want alignment. If you're hiring a salesperson, for example, you want them to be a little aggressive, love talking to people, be friendly and love helping people, and maybe have a bit of a chip on their shoulder. But most of all, you want them to actually want to be in sales.
You want to go to a doctor that reads medical journals in their spare time. You want to go to an accountant that crunches numbers in their sleep.
One time a guy I hired to cut down a tree gave me a half hour lecture on the way trees grow to protect themselves in times of drought. It was obvious that he loved trees and cared about his work.
At the end of the day, you want people whose interests and skills align well with their profession. When you add passion for a job, along with interest and skill alignment, you get those real fantastic career fits, where someone loves their job.
If you're representing yourself to employers, show them that you're going to be good at the job you're applying for. But then also show them why you're going to love what you do.