any of the natural numbers (positive or negative) or zero
"an integer is a number that is not a fraction"
Wikipedia
"When I asked the programmer to round up any fractional values, he simply returned an integer for each result."
In plain English: An integer is a whole number that has no fractional or decimal part.
"Please enter an integer between one and ten to set your timer."
Usage: Use integer to refer to any whole number that does not include fractions or decimals, such as positive numbers, negative numbers, and zero. Avoid using it for rounded approximations when you specifically mean a complete count without partial units.
The word integer comes from the Latin term for "whole," which originally meant something that had not been touched or cut. It entered English as a doublet of the words entier and entire, sharing roots with terms like tact and thwack.