Originally posted by AThousandYoung
Right. I remember something about this, but it sounds like you know more. Can you offer the layman's version?
What I know is from my own field and data filters, so I don't know if it is exact in this case. Anyway, since this is non-technical it might not matter...
In a wave, the peaks will seem to "increase" and "decrease" as the wave moves. Like the wiki illustration here:
You can then see that the wave seems to move faster than its shape, because the highest peak eventually starts "decreasing" and the next peak becomes the largest one. So eventually you'll reach the same shape as before, but with the previous peak being the highest one! The speed of that shape is the group velocity.
Signal velocity is the speed at which a wave carries information. Imagine a disturbance in the wave, that disturbance would move at a certain speed which is the signal velocity. The easiest way to think about it is how fast it gets from point A to B from the moment when you originally send it from A (sometimes also called the front velocity, but it's the same AFAIK).