Legendary Tailed Beasts are powerful demons that were created from the Ten-Tailed Beast by the Sage of Six Paths, but have been sealed within humans to be used as weapons.
In times past, ninja throughout the world continued to wage war against each other and were always looking for new methods of gathering military power and strength. Once such ninja, Hashirama Senju, gained the ability to control these Bijū with his powers and jutsu, even having more than one under his control at a time. He eventually sectioned off and distributed Bijū to each of the powerful nations in an attempt to stabilize the balance of power. This method proved to be ineffectual, because humans began to see these Bijū as nothing more than destructive monsters and demons and eventually sought them out and used them primarily in war time. Because of this treatment, the Bijū began to harbor feelings of hate towards humans and wanted nothing to do with them, distancing themselves as much as they could. In order to better control the Bijū, ninja started sealing them inside hosts and creating jinchuuriki.
Years later, these Bijū were used by Madara Uchiha on two separate occasions against the village of Konoha. The first was when he placed the Three Tails, Isobu, inside the kunoichi Rin Nohara under the guise that once she returned to the village, the beast would be released and wreck havoc on the villagers. The second time was when he gained control of the Kurama with his Sharingan and used the Bijū to aid him in battle as he sought revenge against Konoha and did battle with its leader, Hashirama Senju.
Sixteen years later, a criminal organization called the Akatsuki set out to capture and seal all nine Bijū in an attempt to bring world peace. Their plan was to use the chakra from the Bijū and create an all powerful chakra cannon, one that could destroy villages and countries. Whenever the great nations would go to war against each other, this cannon would be used against them to show them the meaning of pain and intimidate them into living together in peace. This goal was changed, however, when the Akatsuki came under new leadership in the form of Tobi as he used the gathered Bijū to resurrect the Jūbi in order to grant him the Rinne Sharingan, a combination of the Sharingan and the Rinnegan. With his new dōjutsu, Tobi would be able to able to reflect his eye off the surface of the moon and place everyone on the planet in an infinite genjutsu, bringing about world peace and making sure everyone lived the life they wanted to, and to secretly be reunited with the deceased love of his life.
This plan was stopped, however, and the Bijū are now free to live their life however they want. The only ones who stayed in contact with humans are Gyūki and Kurama.
The Bijū each possess immense physical strength and endurance because of their giant proportions. They also possess accelerated healing and vast chakra supplies. They have shown the ability to release shockwaves from their roars as well and devastate the landscape with casual physical strikes.
The Bijū are essentially just masses of Deidarabotchi’s chakra given shape and sentience. Even if killed or destroyed, they will just eventually reform.
The Bijū Bomb (尾獣玉, Bijūdama) is the ultimate offensive technique that is used among all the various Tailed-Beasts, a chakra blast projected from their mouths which can destroy mountains. This is created by molding positive black chakra (+の黒チャクラ, purasu no kuro chakura), and negative white chakra (−の白チャクラ, mainasu no shiro chakura) together. The power is then compressed. The opposing chakra must be balanced at an 8:2 ratio respectively or it will backfire.
Each Bijū seems to have a unique power from the others, such as Shukaku whom is able to control sand whereas Son Gokū is able to create lava, Saiken can produce a powerful corrosive agent, Matatabi can manipulate and produce blue flames, and so on.