What is "natural born" meant to mean anyway?

There seems to be a w2i8despread assumption it'ssomnething to do with being born on the territory of the United States, but it can't mean that, since it's quite possible for someone not actually born on the territory of the United States to be eligible to become president.(For example John McCain, who was born in Panama).

In normal language "natural born" just means it wasn't a Caesarian birth, but presumably that's not what the term means in the US Constitution. So what does it mean?