Black Kurama is a counterpart of the Nine-Tailed Fox, Kurama, and an antagonist who appeared in Naruto Shippuden Movie 6: Road to Ninja. He was sealed in Menma's body, but was later beaten by Kurama and Naruto.
In the alternate world that Naruto and Sakura ended up in, the Nine-Tails has a counterpart called the Black Nine-Tails (黒九尾, Kuro Kyūbi), who is sealed within the body of Naruto's alternate self, Menma. Menma's hatred has allowed him to bond with the Black Nine-Tails, and he is able to create and control living entities composed of its chakra, which are known as the Nine Masked Beasts. He doesn't display any kind of tailed beast transformations during the film, but he is able to completely unleash the black fox, using it in a manner similar to a summon.
At the climax of the film, Menma restored and summoned the Black Nine-Tails so he could finish Naruto off. When Naruto was overwhelmed, the Nine-Tails confronts Naruto that being beaten by a fake, however, not wanting to be trapped into a world controlled by Tobi, it offered a truce with Naruto to work together. Having no other choice, Naruto opened the seal to summon the Nine-Tails in a similar matter to fight against its opposite. In the battle, Naruto was barely able to win, but Tobi revealed that this was his plan, to have Naruto and Menma fight, as doing so would cause the two foxes to fight and weaken the Nine-Tails. As he possessed Menma, the Nine-Tails warned Naruto if he looked into Menma's Sharingan, it would be all over for Tobi planned to extract the fox out of Naruto the same way he extracted it from Kushina.