This is stated in Japanese mythology to be the pinnacle of age and power for a kitsune, and takes at least 800 years to attain, 100 years for each extra tail the kitsune grows as their power and age increases. Kyuubi are supposedly near-godlike in power. The Korean equivalent is called a gumiho/kumiho, while the Chinese equivalent is called a huli jing (although, traditionally, kumiho are much more likely to be murderous and evil than playful and nice, and may not always have nine tails despite the hanja/hanji being that for "nine-tailed fox").
