Competence to me is a combination of a strong amount of pragmatism, common sense, creativity and no panicking when running into something they are not immediately equipped to handle. They usually focus on solutions instead of getting caught up in the scale of the problem, and are present in the moment. If the world were ending and someone was bleeding they would bandage the wound while looking for immediate safety, if they were facing aliens without weapons they would be focused on hiding, then shelter, then resources.
Basically competence is clarity, the ability to see which issues can actually be resolved and resolve those.
Edit: An everyday example would be the difference between someone who when their car breaks down freaks out and spends 10 minutes lamenting their fate, and the person who calls AAA. Neither knows how to fix a car, one person acknowledged it before there was a crisis and took steps to prevent it from being a crises. Or if you have a broken pipe and you try to fix it but fail vs the person who has a plumber in their phone; you don't have to fix a problem personally, you just have to know a way a problem can be fixed and be ready for it.