An integer is a number that has no fractional part, and no digits after the decimal point. An integer can be positive, negative or zero. (Compare this to real numbers than can have digits after the point and can have fractional parts)
Example integers: 12 , 34 , -4 , 0
The following are real numbers and are not integers:
Whole numbers (sometimes called 'counting numbers') are like integers, but they cannot be negative. They are usually used to indicate the number of objects. Example: 12 students.
Real numbers can be converted to integers by rounding. This means removing the decimal digits and adjusting the result to be the nearest integer to the original number.