How could relaxing reduce pain? Well, the uterus is built of two opposing types of muscles: longitudinal muscles, which are mostly on the top of the uterus; and circular muscles, which form the lower half of the uterus. During labor, or monthly cramping, for that matter, longitudinal muscles contract to clear things out, but if a woman tenses up, the circular muscles lower down "close the outlet, maintaining the uterus in its unemptied state. ... Then the muscles that empty the uterus and the muscles that hold it closed are working
against each other" (Childbirth Without Fear, Grantly Dick-Read, M.D., p. 67) and pain results. Just as it can become painful when the bladder needs to be emptied but the timing isn't convenient, so there is unnecessary pain when half of the muscles of the womb are trying to clear out the uterus but the other half are tense and constricted.
UPDATE 2/13/13: Ina May Gaskin, in her book Ina May's Guide to Childbirth, recommends blowing "raspberries" or "horse lips" to effectively relax the mouth (and therefore the cervix as well). To do this, completely relax your lips and blow a good amount of air through, letting your lips flap lips together. She writes, "Women who have tried this during menstrual cramps have found it surprisingly helpful in alleviating pain" (p. 180).
Relaxing into the pain instead of resisting it will allow your body to do what it is designed to, with the least discomfort. Try it this month when your "way of women" comes visiting and let us know (in the comments below) if the childbearing mothers' strategy works for your monthly "housekeeping" as well! This could be quite the discovery. If it works for labor contractions, why would it not for menstrual cramps?