Natural zero basically means "There isn't any..."
E.g. Height, Weight have a natural zero because you could say "there isn't any height, there isn't any weight, etc."
If "zero" is taken to mean something else besides "there isn't any", then it is not a natural zero.
E.g. Years - Year 0 is an arbitrary point in time, and it is so named because it was convenient to use the year Christ was born as a zero.
Temperature - is an arbitrary temperature, and it is so named because it was convenient to use the freezing point of water as a zero.
Does that make more sense?