I tried to find a satisfactory definition for "natural language" but the only thing I found was related to computers. In that field, natural language is defined as human language.
It seems that for a language to be "natural" it would have to be instinctive and not require any modeling, instruction or training. People would be born with a language, and as soon as their fine motor skills allowed, they would be using it.
Language isn't acquired or used in a vacuum; it's a mode of communication used amongst people groups. Even if someone talks or signs to himself, or writes down private thoughts in a diary, the source language is usually one that a group, not an individual, uses. The exception would be a code that one creates for one's own private use but that's not language in the sense of communicating with others.
Just my ramblings.
Still, I'm curious as to how others define "natural" language. I've probably overlooked something.