I think that the essence of being a coder is being willing to solve, with absolute precision and certainty, a problem that is at first glance poorly defined and/or seemingly difficult or impossible.

So, with that definition, you've got to not only be curious, but also tenacious in the pursuit of solutions.

If you're the type of person who is satisfied with just pressing a button and having something work, and have never paused to wonder about the why, then programming is not for you.