Overhead Light Fixture - Didn't Use Green Screw
The reason for grounding to the electrical box is so that the whole system is grounded. If the box is not grounded then there if the hot touches the box, then the box will become energized. This creates two possible problems:


If the hot box is in contact with wood (like house framing), then it can leak electricity into the wood at high resistance. This will cause the wood to get hot. If it gets hot enough, it could start to burn.
If anybody touches the box, or anything connected to the box, they could be electrocuted. For example, you know those little screws that screw the switchplate over the switch? You know what they screw into? That's right, they screw into the box. So if the box is hot, then those little screws are hot too.