Nitpick - it's "prodigy", plural "prodigies".

My brief attempt to outline one possible explanation for the phenomenon.

Read if you not familiar with search algorithms/spaces the wikipedia article on it.

Imagine trying to find a good piece of music, you could just create random notes and see how good they are, but that wouldn't be very interesting music. So instead you have to have an algorithm to generate interesting pieces of music. The algorithm might take a small piece of work and build upon it.

I didn't say where the algorithm came from, likely we build it in some way as we get experience. This building of skills is in turn is another search problem, that of finding good specialist searches. So in answer to your question, the gifted people might be those that are lucky and find good search algorithms (at a variety of different levels).