A real world example of an absolute value function is any calculation in which the total depends upon simple addition of all the quantities in the function, regardless of sign. One example of such a calculation is the number of feet traveled by an athlete running around a race track.
When calculating displacement in the usual way, the function called for assigns the positive sign to one direction and the negative sign to the other. For instance, it may assign north as negative and south as positive. This is so that a person traveling the same distance in both directions results in a total displacement, or distance traveled from the starting location, of zero. However, when finding the total distance traveled without regard to the starting location, absolute value is used. This is so that if athletes run around a track a certain number of times, they can calculate the amount of exercise from one session.