This is how I understood it from schooldays, I'm sure someone who was born since the Romans will have a better explanation.
Activated charcoal is, or contains a large amount of, animal charcoal. It is usually "microfined" - that is to say it is ground into extremely fine particles.
It has the property of "adsorption" - that is to say some gaseous elements will adhere closely to it's surface. This is why and how carbon filtering can be used for gasmasks, gases such as chlorine stick to the surface of the carbon particles and do not pass through the filters.
It was also sold at "decolourising charcoal" when I was younger, liquids with colour (like tea and coffee) could be filtered though it and end up colourless. (and tasteless as well).
That's probably not a scientific explanation, but it might help, if you can add some other research to it.
(Added later) - I forgot this bit. It is also (on a microscopic level) highly porous, making the surface available for adsorption much greater than otherwise - I think that is where the "activated" thing comes from.