The nine-tailed fox had nearly destroyed Hidden Leaf 12 years previously. It is one of the "bijuu", a tailed beast of the ancient world. It took the sacrifice of the Fourth Hokage to imprison the demon and place it into the body of the young baby Uzumaki Naruto. It was the Fourth's hope that the Leaf villagers would look at Naruto as a hero for serving as the vessel to contain the demon. However, the people of leaf village see Naruto as the Kyuubi itself and shun him.
Even though it is one of the Bijuu, Kyuubi can be controlled by several individuals, including Shodai Hokage and the Mangekyou Sharingan of the Uchiha. It was the powerful Mangekyou ability which some said allowed Uchiha Madara to tame the Kyuubi. His control of the beast is what allowed him to direct it to attack Konoha around the time of Naruto's birth. Kyuubi would recognize Madara's cursed bloodline again in the future when Uchiha Sasuke used his Sharingan to peer inside the prison holding him inside Naruto.
The power of the Kyuubi has affected Naruto in several ways physically. When Naruto's body becomes injured, the power of the Kyuubi will leak out and heal Naruto's body at a very quick pace. Also, when Naruto experiences emotional experiences the chakra and power of the Kyuubi begins to leak out and turn Naruto into a more feral individual. At first he had little control over the ability to draw on the Kyuubi's chakra, but the Sannin Jiraiya taught Naruto how to reach deep inside himself and convince the Kyuubi to give him extra chakra when needed. This large amount of additional chakra allows Naruto to perform Kage Bunshin on a very large scale and also summon the Toad Boss Gamabunta. Kyuubi remains a reluctant prisoner within Naruto, stubbornly saving Naruto with his chakra only out of necessity to protect his own life.
The Akatsuki criminal organization has expressed interest in obtaining the Kyuubi from Naruto for their own diabolical ends, though they have yet to accomplish this goal. Demon imbued persons are called "jinchuuriki" by Akatsuki, literally "the power of human sacrifice". This seems to stem from a life being lost when the demon is imbued into the individual. For Naruto, Yondaime Hokage gave his life to imprison Kyuubi.