Example: I'm sneaking around and find a group of supermutants together. I use my sneak attack to kill one of the supermutants. My status changes to "caution" since they heard my shot and saw one of their own die by my hand but they do not see me. I hide by a rock. Without the perk, the supermutants search the origin point of the shot and the area around it, increasing the chance of one of them finding me, it takes a while for me to recieve a "hidden" status again. With the perk, the time it takes for the mutants to stop searching for me and achieve "hidden" status again is drastically reduced.
Does that help explain it?