Coming from a woman who has been having her period for over 16 years, there are a lot of cycles that women go through that can have an effect on their emotions. The reproductive cycle is a pretty strong one, but
it varies from woman to woman as others mention.
To give a more general answer, the reasons a woman will sometimes be emotional during her period vary.
After 16+ years of bleeding from the crotch monthly, for
me, those reasons are a direct result of menstruating. I usually start the cycle off on the first day of menstruation with mild to extreme cramps depending on any number of reasons from digestive regularity to hot weather. I also feel filthy and unattractive until I don't have to protect my undergarments anymore. The psychological effect of feeling filthy and unattractive can be really bad, especially in younger women, who are already vulnerable to questions of self-image.
This feeling that women know about and men don't seem to find as obvious, is made a little more clear when you see that every feminine menstrual product (tampons, pads, cleansing products) have a similar advertising message. That using the product will make you feel as clean as normal, you'll be able to participate in sports and what not with no discomfort, and that you'll be every bit as lovely as a woman who isn't on the rag.
There are other reasons for emotional sensitivity, but this is probably the biggest one. Basically, the feeling of being unclean for days at a time makes women vulnerable. The associated physical discomfort can make it worse.
Also, the situation of being hypersensitive during the menstrual period is
not Premenstrual Syndrome.
The provided link doesn't have all that much to do with my explanation, but it notes some effects of menstruation on non-reproductive systems in the body.
http://en.wikipedia.org/wiki/Menstrual_cycle#Effect_on_other_systems