Gene spliced creatures made to order. These can range from customized humans to totally new beings made with the desired combination of traits. Furry fans like to read and write stories involving any of those creatures, admire and create art featuring them, and play games that include them. Furries are those who get into the concept so much that they deliberately develop alternate personas that actually have those animal traits. Each persona takes on a life of its own in a sort of controlled schizophrenia such as ventriloquists and fantasy gamers practice.
Furries have many different ways to relate to their furry personas.
Some think of them as totally different beings who happen to live inside them. Others see them as simply minor varients of themselves. And still others see them as vehicles for normally suppressed aspects of their own personalities. The most interesting way of viewing a persona, though, is to see it as some sort of mystical entity that can confer benefits which are represented by the animal shape. Some relate this to a witch's familiar or to the spirit guardian of the Plains Indians.