An integer is a whole number and can be positive, negative or zero.
The natural numbers (the numbers we use to count) are positive integers: 1, 2, 3, 4, etc.
Multiplication tables learned at school are based on integers.
A prime number is always an integer.
A factorial is always an integer.
All rational numbers can be expressed as the quotient of two integers. For example: 2/7 is a rational number, but √2 cannot be expressed as such a quotient so √2 is an irrational number. Pi (π) which relates the diameter of a circle to its circumference is also irrational. The rational number 22/7 is often used to represent π, but it's only an approximation because π is irrational, and π belongs to the transcendental numbers.