What is the meaning of natural in counting number?

Answer 1

Counting numbers are the positive integers starting with 1. Some people use the term "natural numbers" interchangeably with that, some people maintain that the set of natural numbers includes zero, like the set of whole numbers.

Answer 2

It is the name given to the set of counting numbers. They are used to count naturally occurring objects or events. Other sets of numbers are less common in nature.

Also, there are several species of mammals and birds (and others?) that are aware of small numbers and can use them.