The analogy I can come up with, based on your post, is of something like addition. We don't know how we add numbers in our heads; but we somehow do it. Some people can do it very, very quickly[1], but won't be able to explain how they did it. On the other hand: a computer doesn't look at digits and numbers; it just looks at bits and shifts them around as appropriate.

[1] https://en.wikipedia.org/wiki/Shakuntala_Devi