Whole numbers are the numbers you learned when you were first learning to count - one, two, three, four, five and so on, all the way up to billions and trillions and past that. In addition, zero is a whole number, and so are all the negative numbers: minus 1, minus 2, and so on. There are an infinite number of whole numbers, running along the number line in both directions.
Why bother calling those whole numbers? Why not just call them numbers? Because there are also another kind of numbers, which we call fractional numbers, or fractions. Whole numbers are numbers that are not fractions. Another way to think of whole numbers is that they are fractions with one as their denominator.