Something that's furry is covered with fur, or a thick coat of hair. Unless she's one of the unusual hairless breeds, like a Sphinx, your cat is probably furry.
Most mammals are furry, in fact, while reptiles tend to be scaly instead. Santa Claus is famous not just for wearing a furry red and white suit, but also for having a long, furry beard. Anything with a surface that resembles fur is furry, from a furry sweater to the furry leaf of a plant.