From the City of Portland Office of Transportation:
The bike box is an intersection safety design to prevent bicycle/car collisions, especially those between drivers turning right and bicyclists going straight. It is a green box on the road with a white bicycle symbol inside. It includes green bicycle lanes approaching and leading from the box.
The main goal is to prevent collisions between motorists turning right and cyclists going straight. It's all about visibility and awareness. At a red light, cyclists are more visible to motorists by being in front of On the Move video screen shotthem. At a green light, the green bike lane through the intersection reminds motorists and cyclists to watch for each other.