This Vulpix is a Fire-type Pokémon owned by Suzie, which was given to Brock for a while.
Through seeing the care that Brock went into in looking after Pokémon, Suzie decided to let Brock look after it. Brock was often seen grooming it and sometimes used it in battle, mostly however in training with Ash. Vulpix, while a little bit spoiled, did enjoy playing about with the other Pokémon. Eventually Brock met up with Suzie again and decided that Suzie should keep Vulpix at the Pokémon Beauty Show.