The idea behind anthropomorphism is that of attributing human characteristics to nonhumans — gods, animals, or inanimate objects. If you believe that your cat wants to celebrate his birthday, you are participating in anthropomorphism.
The Greek words for "human" and "form" created the word anthropomorphism, originally used to give human qualities to a deity. The Greeks and Romans used the idea in stories about their gods, giving them human traits to balance their powers (and make better stories). Even today, many people picture the god they worship as a human form. Whether it's an old man with a beard, mother earth, or a bearded lady, that's anthropomorphism.