Anthropomorphic comes from the Greek - anthropos meaning human, and morphe, meaning shape - and involves attributing human characteristics such as giving them a humanoid shape, speech, emotions, ideologies, etc. to non-human things - animals, plants, abstract concepts, forces of nature, etc. Examples of these in comics include:
One of the more common versions of this in comics, and the one most comic readers mean when they describe a title as an Anthropomorphic comic, is zoomorphism, involving humanoid animals.
Famous zoomorphic examples:
As well as the above examples which feature worlds primarily peopled by zoomorphic animals, there are also examples of such beings on worlds predominately populated by regular humans, including
Influence Outside of Comics
Fans of the genre often attend conventions dressed in "fursuits" or other cosplay costumes which feature some sort of anthropomorphic character, or animal ears, paws, and tails added to their clothing.
Furry Conventions in the United States of America