The Equipment Grounding Conductor serves 2 distinct functions.
1. It connects all ungrounded metallic parts to the earth via the bond to the grounding electrode conductor at the service.
2. It a path for the ground fault to follow to the source, facilitating the opening of the overcurrent device.
(see the revised definition in Art 100 of the 2014 NEC, as well as the informational note following it.)
Most people associate it with #2.
I also believe it would serve better purpose to change the name to EBC, but there is still some resistance due to the above statement I have provided.