There is no proven scientific reason...but I found this, courtesy of MSNBC:

"The most plausible explanation, and the one that is taught in medical school, is that we yawn because oxygen levels in our lungs are low. Studies have shown that during normal, at-rest breathing, we don’t use anywhere near our lung capacity; for the most part, we just use the air sacs at the bottom of the lungs. If the air sacs, called alveoli, don’t get fresh air, they partially collapse and the lungs stiffen a bit. As a result, it’s believed, our brain prompts the body to either sigh or take a yawn to get more air into the lungs."