They do two things. First, you get right of way (so highest priority). Second, the only cars they do not stop are right turns. As other commenters have mentione

They do two things. First, you get right of way (so highest priority). Second, the only cars they do not stop are right turns. As other commenters have mentioned, the point is to improve efficiency, both since cars can turn right once there are no pedestrians, but also since pedestrians can cross for a longer period of time. On the other hand, it can also be annoying for cars, since they often never get a dedicated right turn without pedestrians. Honestly I think stop lights aren't a big danger for pedestrians. Crossing at intersections with stop signs is far, far worse -- drivers have to pay attention to multiple directions of traffic as well as pedestrians.