An animal, mammal, who is fuzzy (bushy, fluffy, hairy, etc.) and/or cute. Usually such a creature makes you want to hug, squeeze, or pet them. Often such animals are used as pets such as dogs, cats, hamsters, guinea pigs, etc.
Mom:That squirrel is so cute! Look at that bushy tail!
Morgyn:It's a fuzzy-lovin'!