Animal dander is loose skin cells (like dandruff) from animals such as dogs and cats. These skin cells contain saliva or other material from the animals. The cells float in the air. If you are allergic to animal dander, when you breathe in the cells you may have an allergic reaction.
Animal dander causes the allergy, not animal fur or hair. The length of the fur on an animal does not affect how allergic you are to an animal.