A natural number is the sort of number that is commonly used for counting or basic arithmetic. They are positive whole numbers, such as one, two or three, and are used to denote quantities in everyday life.
There are many different sets, or groups, of numbers that are defined by mathematicians. Mathematicians disagree on whether to include zero as a natural number, but in general, these are the sorts of numbers that most people encounter in their earliest math classes. Natural numbers are not fractions or decimals and are not negative.
The term "natural number" is used to distinguish this group of numbers from others. Whole numbers are a group of numbers that include all the natural numbers and zero; by some mathematicians' reckoning, the two terms are synonyms. Integers are a group of numbers that contain all the natural numbers and the negative whole numbers as well. Rational numbers include all integers plus fractions. There is a group of numbers called imaginary because they produce counter-intuitive results when squared.