Here's a Wikipedia article that lays out some useful info: http://en.wikipedia.org/wiki/Activated_carbon

It seems (from the info above) that activated charcoal/carbon is the stuff left by fire that hasn't fully burned.

Ash, of course, is a different item, with its own uses.

Charcoal from a campfire has been suggested for addition to questionable water (on the theory that it will absorb a variety of toxins and foul odours/tastes). As I recall, boiling with charcoal in the water is the preferred method.