A natural number is a number that is used to count items. For example, you could count the number of fingers you have, the number of cars there are in your house, or the number of students in a classroom.
The natural numbers, also called the counting numbers, are the numbers 1, 2, 3, 4, 5, 6, ...
In elementary school, children learn to count using the natural numbers and it is natural for them to start at 1.
It probably makes more sense now why 0 is not a natural number. It is natural or it makes sense to count when there are things or items to count. When there are no items (or zero), no one cares about counting.
For example, suppose your favorite activity is to count stars at night. One night you are looking up and you do not see any stars, will you try to count anyway? Of course not!
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