The Balinese is breed of domestic cat with long hair and Siamese

Siamese (cat)

The Siamese is one of the first distinctly recognized breeds of Oriental cat. The origins of the breed are unknown, but it is believed to be from Thailand. In Thailand, where they are one of several native breeds, they are called Wichian Mat...

-style point coloration. It is essentially a Siamese but with a medium-length silky coat, and a plumed tail.
The "Balinese" is not actually from Bali

Bali

Bali is an Indonesian island located in the westernmost end of the Lesser Sunda Islands, lying between Java to the west and Lombok to the east...

 or any part of Indonesia. It is not a natural occurring breed, but originates from human-controlled breeding efforts.

The Balinese was originally registered as a "long-haired Siamese", and examples were known from the early 1920s.