integer – a whole number; a number which is not a fraction
(pronounced in-tuh-ger)
To remember the meaning of integer, use the following mnemonic:
She was into German (integer) but she could only say the first 10 numbers.

An integer can be positive, negative, or zero, but it must be a whole number and so therefore cannot be a fraction or decimal.
Example 1

Here -4, -3, -2, -1, 0, 1, 2, 3, and 4 are all integers and yes zero is an integer.
Example 2

These are all integers.

These are NOT integers