According to psychologists Andrew Gallup and Gordon Gallup of the State University of New York at Albany, that is why we yawn: to boost blood flow and chill the brain.
Not only that, brain-cooling explains why you can "catch" a yawn, says Gordon Gallup. "We think contagious yawning is triggered by empathic mechanisms which function to maintain group vigilance." In other words, yawn-catching evolved to help raise the attentiveness of the whole group.