An example of using an integer as an absolute value in real life is describing the distance, to or from something, using a whole number. For instance, someone would say they are 5 miles from Tucson or 5 miles past Tucson. In both cases, the person would be describing the distance as a positive number.
Integers are numbers that do not have fractional components. They include both positive and negative numbers, as well as zero. Absolute value is the distance a number has from zero. For instance, 2 and -2 both have an absolute value of 2 because both numbers are a distance of 2 from zero. The absolute value of any positive or negative integer is always a whole number, which means a positive number greater than zero.
Expanding on the example of describing the distance from Tucson, Tucson represents zero on the number line since it is the destination. Once the travellers reach Tucson, they are no longer any distance from Tucson. If they accidentally drive past Tucson, they wouldn't describe their location as being a negative distance from the city, even though it could be drawn that way on a number line. Whether they are 5 miles from Tucson or 5 miles past Tucson, the distance is always 5 miles, not minus 5 miles. That makes it a real-life representation of an absolute value.