It's no longer enough to just be a doctor.
This sentiment echoes loudly throughout the corridors of medicine today. At one point, you could just be a clinician. This has changed. Doctors are no longer able or expected to know everything. Atul Gawande has (rightfully) expressed how the medical culture must shift away from a culture of lone rangers to a pit crew model to limit costs and improve outcomes. With strong data in favor of this model, it is shown that medicine needs technicians, not thinkers.
Residencies and fellowships are catching up to this idea. For the most competitive jobs and fellowships today, you have to be more. You need to fill a niche. You need some combination of strengths which makes you irreplaceable.
So, what does it mean to be a "gunner" today? Well, if it means being competitive in your field, then it means offering something unique. Medicine needs leaders and powerful communicators. It needs people who have presence and can affect those around them -- both their peers and their patients. This unifies the field of medicine and strengthens the relationship between doctors and patients. So, residencies (and even more so, fellowships) look for individuals who they can groom into leaders.
As always, competence and ability to pass exams is important -- but critically, it is assumed that you can do these things already. If you can't yet, then you should focus on that. But once you've achieved a certain level of competency, being a "gunner" is showing you can be a leader and innervate those around you.
So, are you a "gunner"?