Kurama

The is the most powerful of the Tailed Beasts; a single swipe of one of its nine tails can raise tsunamis and flatten mountains. After the demon fox attacked Konohagakure, Minato Namikaze, the Fourth Hokage, sealed it within his newborn son, Naruto Uzumaki, by using the Dead Demon Consuming Seal, sacrificing his own life to do so.

Background
The demon fox is an age-old natural disaster, appearing at random to attack areas where human malice collects and festers. Many years ago, when Madara Uchiha defected from Konoha, he used his Mangekyo Sharingan to control the demon fox and used it to help him fight against Hashirama Senju, the First Hokage, for revenge. The battle was so great that it tore the earth apart and it created the Valley of the End. However, despite controlling the demon fox's power, Madara was defeated.

Many years later, Madara used the demon fox again to attack Konoha (although Madara denied this, and he claimed that the demon fox's attack was a "natural occurrence"). During the attack, the demon fox decimated all the shinobi that came to repel it. Minato, riding atop Gamabunta, was able to defeat the demon fox by sealing it within Naruto, which freed it from Madara's control. In the anime, it was revealed that the demon fox had left behind large amounts of its chakra during the attack. Kazuma, hoping to make use of its power, sealed the chakra within his son, Sora.

Personality
The demon fox is a giant beast of mass destruction and almost pure malevolence. It is also intelligent, and has a sadistic and sarcastic personality. However, it does have a distinct sense of honor and pride, and possesses a loathing respect for Naruto and Minato.

At first, the demon fox relished the thought of killing Naruto, but it soon realized that it shares the same fate as Naruto as long as it's sealed within him, so it has to cooperate with Naruto or it will die. It will even go to great lengths to preserve its own life, as shown when it forces its chakra into Naruto whenever his life is in danger. Later in Part II, the demon fox became angry and contemptuous at Naruto when he rejected its chakra, though this is merely the rage of missing the opportunity to usurp control over Naruto's mind and body and thus weakening the seal. However, it will back down if Naruto threatens to harm or kill himself.

The demon fox has a deep hatred for the Uchiha clan and their Sharingan, likely because of the many times Madara has manipulated it in the past. It even remarked that Sasuke Uchiha's eyes and chakra are more sinister than its own, because his Sharingan reminded it of Madara. According to the third Naruto databook, the demon fox is the only one who knows the truth about the Uchiha clan and about Naruto. However, it appears that the demon fox has no intentions of telling what it knows.

Part I
Naruto is not made aware of the demon fox's presence within him until twelve years after its sealing. He first makes use of its chakra during his battle with Haku. Believing Haku to have killed Sasuke, Naruto gives into anger and entered into his Jinchūriki form to defeat Haku. He didn't realize that this was the demon fox's chakra until he is later taught to take advantage of it by Jiraiya. To force Naruto to call upon the demon fox's chakra and enable him to use the Summoning Technique, Jiraiya throws Naruto off a cliff. To save himself, Naruto enters his subconscious and meets with the demon fox for the first time. He demands some of its chakra as "rent" in order to save them both, and the intrigued demon fox, complies, allowing Naruto to summon Gamabunta.

Naruto takes advantage of the demon fox again during his fights with Neji Hyuga and Gaara, requesting some of its chakra to help him with the battles. Later, when Kabuto Yakushi severs Naruto's heart muscles and the neighboring Chakra Pathway System, the demon fox is unable to heal the damage. It, like Naruto, has a near death experience, something it is slow to recognize. Naruto and thus the demon fox are saved by Tsunade. During his battle with Sasuke at the Valley of the End, the demon fox gives Naruto enough chakra to attain the one-tailed transformation, something the demon fox indicates he should be grateful for.

Part II
During the timeskip, Jiraiya weakens the demon fox's seal with the key in order to give Naruto more access to its chakra. This has the side effect of allowing Naruto to achieve tailed transformations with little provocation. When the three-tailed transformation is proven insufficient in a fight with Orochimaru, Naruto gives in to the demon fox and enters his four-tailed transformation. The demon fox gains control of his senses and attacks all around him, both the likes of Orochimaru and Sakura Haruno. After its influence is suppressed by Yamato, he tells Naruto how the four-tailed form caused him to attack Sakura, someone he cares about. Naruto resolves not to use the demon fox's power again.

Soon afterwards, when Naruto meets Sasuke again for the first time in a few years, the demon fox tries to offer Naruto some of its strength. He refuses, but before it can put up much of a fight, Sasuke appears within Naruto's subconscious. Surprised, the demon fox commented that Sasuke's eyes and chakra are more evil than its own and he is just like Madara Uchiha. Sasuke suppressed the demon fox back to its cage, and the demon fox struggles to warn Sasuke not to kill Naruto. It sees little activity after that, surfacing within some of Naruto's shadow clones that grow frustrated with the wind element-training. In the anime, the demon fox reacts to its chakra stored within Sora. Naruto is able to keep the demon fox from taking control of his body, but it manages to take back all of its chakra from Sora.

Later, when Naruto tries to learn senjutsu, the demon fox prevents Fukasaku from fusing with Naruto, wanting Naruto to use its chakra instead of Sage chakra. It is given an opportunity to appear during Naruto's battle with Pain. After Pain appears to have killed Hinata Hyuga, Naruto slips into his six-tailed transformation, which the demon fox used to its advantage by destroying the First Hokage's Necklace. When Naruto was captured by Pain's Chibaku Tensei technique, the demon fox tempts Naruto to give his heart to it so it could destroy everything that was causing Naruto pain, thus distorting the seal to the point where the eight-tailed transformation is released. Before it can convince him to completely remove the seal, the spirit of Minato appears in Naruto's subconscious to stop him. Enraged, the demon fox tries its best to kill Minato for revenge, but Minato ignores it, soon afterwards restoring the seal to its original strength. Once Pain is defeated, Naruto confronts Pain's base mind, Nagato, and is able to simultaneously use Sage chakra and the demon fox's chakra, combining the two different pupil appearances.

Activity inside Naruto
As the demon fox's Jinchūriki, Naruto has accelerated healing, unrivaled stamina and speed, massive strength, and access to the demon fox's near-limitless chakra. The demon fox's chakra allows Naruto to perform his signature jutsu, Shadow Clone Technique, seemingly without limit. He is even able to summon Gamabunta, a normally Kage-level feat requiring a huge amount of chakra proportionate to the size of the summoned creature.

Although the demon fox's chakra naturally mixes with Naruto's own, Naruto can forcefully tap into the demon fox's reserves. After training with Jiraiya, he learns to request some of the demon fox's chakra for his own use. Alternatively, and what has become the more common method over time, he can give into anger or frustration, allowing the demon fox to force its influence upon him. Depending on how much of its chakra he gains, Naruto can lose control of his senses, only to devolve into an animal that attacks anything within reach. For this reason, Naruto learned to exercise more control over the demon fox's chakra.

A number of methods have been devised to break the demon fox's influence over Naruto: Yamato can use the Hokage-style Sixty-year-old Technique - Kakuan Entering Society with Bliss-bringing Hands, which is facilitated by the necklace Naruto wears; a Demon Fox Chakra Seal can be applied to Naruto's body; an Uchiha can enter Naruto's subconscious and force the demon fox to recede. The most effective of measures, however, is Naruto simply limiting his use of the demon fox's chakra and not allowing his anger to get the better of him.

The Seal
Jiraiya revealed that when Minato sealed the demon fox within Naruto, he split the demon fox's chakra in two halves, the Yin and Yang. He sealed the Yang part within Naruto with the Eight Trigrams Sealing Style, and sealed the Yin part with the Dead Demon Consuming Seal, thus making it inaccessible to Naruto.

Within the seal, it is depicted as a kind of basement of a boiler room or a power plant, with pipes lining across the ceiling and the floor being "flooded" with water. The water level indicates how much of its chakra Naruto is using. On the entrance gate of the demon fox's cage, there is a parchment of paper that says, which serves as a "lock" to keep the demon fox in.

Hiruzen Sarutobi and Kakashi Hatake allude that if Naruto loses all control of the demon fox's chakra, the seal will break and the demon fox will be released. Though the seal is unlikely to break on its own; the chances of it happening increase as Naruto draws upon more of the demon fox's chakra. The seal naturally weakens over time, something Minato created a key, Gerotora, to remedy. Jiraiya instead used Gerotora to "twist" the seal a little, which inadvertently caused more of the demon fox's chakra to leak out and unleashed the four-tailed transformation. As the seal weakens, Naruto's transformations occurs much quicker and with greater intensity, often against his own will. As seen during Naruto's Part II training sessions, even the slightest amount of frustration on Naruto's part allows the demon fox's chakra to leak out of the seal, which will then rapidly progress to his four-tailed form, or onwards.

The seal also has a final safeguard to prevent the demon fox from escaping. Minato made it so that if Naruto ever transforms into his eight-tailed form, Minato will appear in his subconscious in order to prevent the seal from being broken. Furthermore, Minato can restore the seal to its normal state, but he stated that he can only do it once.

Influences
A is a well-known character in Japanese folklore, and the influence behind not only the demon fox, but many other reincarnations in modern Japanese culture. It likes to play pranks on people, and on occasions, transforms itself into a beautiful woman and seduces men (obviously the inspiration for the Sexy Technique). However, kitsune are known to keep their promises, a trait Naruto has; his ninja way is to "never go back on his word." It is also noted that every time Naruto loses control and is overwhelmed by the demon fox's chakra, he gains another "tail" of chakra. This stems from the belief that the more tails a kitsune has, the more powerful it is, with nine tails usually being the limit.

It might also be noted that according to Chinese mythology, the last king of the Shang Dynasty was seduced by a beautiful, but malevolent nine-tailed fox spirit, which eventually resulted in his downfall, and this could have been another source of inspiration for the demon fox.

Trivia
Many fans incorrectly believe the demon fox's name is "Kyuubi," the direct English pronunciation of "Kyūbi." When the demon fox is referred to, it is usually called "Kyūbi," which just stands for "Nine-Tails." This is similar to the belief that Minato Namikaze's name, before being revealed, was "Yondaime," which means "Fourth."

Quotes

 * "(Laughs) Well I suppose I can't kill you, can I? After all, you die, I die. Your courage is most impressive little boy... very well, as a reward for making it this far, I will loan you my chakra!"
 * "You runt... you really are weak! (Laughs) You better be grateful to me... and to your beloved Fourth Hokage, who sealed me inside a twerp like you!"
 * (To Sasuke) "Eyes with such power and chakra more sinister than my own... you're just like Madara Uchiha."
 * "Destroy everything... destroy everything that hurts you... give your heart to me... I will save you from the pain."