Fursona is a furry fandom slang term that refers to the concept of a furry-themed persona.
People actively involved in furry fandom often have one or more alter egos by which they represent themselves. One of these characters may be a "talking animal" version of its creator, or, in other words, an anthropomorphic animal persona. This character is called a "fursona".
Common practice
The process of creating a fursona is one of the first steps of entering the furry community, or at least de-lurking into it. It generally consists of the newcomer choosing a specific animal with which he feels a particulary strong identification.
The chosen fursona might change in part or entirely. A feline furry fan might oscillate between several species in the family; or a kitsune fursona can grow a new tail. It's only important that the main role of the fursona (an iconic representation of its creator) remains intact.
See also: Furry lifestyler