Furry music is a term that is often used to describe music (of any particular genre) that is either performed by self-described members of the furry fandom, or centered around themes of a furry nature, or both. There is dispute about whether the former should qualify.
Music within the furry fandom
The term "furry" has historically and primarily been used to describe a readily-recognizable genre of visual art, often to the point of synonymity. Unsurprisingly, manifestations of typically furry themes in other artistic media (i.e., literature and music) have figured in lesser levels of prominence, and such alternative media are in lesser quantity of material than that of visual furry art.
Nevertheless, music within the furry fandom exists, as a number of furs happen to be musicians and singers; some have often performed their work at conventions (even going as far as to serve as DJs at dance raves), while others have released their work online for sale or free distribution.
Web sites such as YouTube are where most furry music can be found and viewed completely free. Not all furries have to go to a convention to share music, some can't even afford a fursuit. Many furry music YouTubers are out there, such as NIIC, Furry Music, Duke. Here are the links to these popular channels:
Furry Music: https://www.youtube.com/c/FurryMusicOfficial