One of my young students is a "natural." What do you think that means?
It might be simpler to contemplate what it doesn't mean. She does not have physical facility: playing the piano does not come easily to her - she can't just sit down and rattle things off.
But her grasp of musical process is profound and entirely self-generated. She is responsive to the tiniest subtleties of timing and tone. For example, she knows that vocal sound and piano pitch are not the same; she even said at one point (with considerable anguish) that she found this "confusing." (It is!)
For her music is too central to be on display all the time. She is the kind of child who dreams music.
I have taught others who, like her, get fascinated by certain songs and continue to work on them over long periods of time--really work on them, not just repeat the same thing over and over.
The challenge in teaching such a child is to get her to trust the depth of her gift so that she does not let it get steam-rolled by competition, which is just another word for conformity.