arcing (short to ground)
sorry, that's not what AFCI is for; that's just the first thing that
came to mind when I though ARC. My bad!

Short-to-ground is protected by a regular breaker. You'll get nice fat
spark if you do this, but you don't need AFCI to detect it.

AFCI tries to detect all the other types of arc that don't trip an
overcurrent breaker.

They accomplishing this by watching the waveform and figuring out what
a bad arc looks like.

They actually have an algorithm (computer program) to detect this.

Again, from the consumer products safety commission:
http://www.cpsc.gov/volstd/afci/AFCIFireTechnology.pdf

Again, sorry for the sloppy (wrong) definition of arc earlier!