In the Naruto universe, there are nine giant demons called the Tailed Beasts (尾獣, Bijū) that inhabit the planet. They are actually living chakra in physical form, often referred to as "Chakra Monsters". The Akatsuki organization has a plan that involves the capture of the Tailed Beasts.
The Tailed Beasts have been around before the First Great Shinobi War. Because of their immense power, the shinobi from each nation tried to use the Tailed Beasts as military weapons during the Shinobi Wars. After the Wars, Hashirama Senju, the First Hokage, managed to capture and control them with his Wood Release techniques, and used them as a peace treaty to the other great shinobi nations, in order to stabilize the balance of power between them. After his death, however, the shinobi nations couldn't control these giant demons themselves and they began to run wild. Their attempts to capture them and harness their immense power failed as no nation could control such power. Instead, the nations moved to capture the Tailed Beasts and seal them within humans, which they were called Jinchūriki. This method worked by the time period of the series.
The Akatsuki is currently in the process of extracting the Tailed Beasts from their hosts in their attempt to create a weapon powerful enough to wipe out an entire country. The only two Tailed Beasts that are not currently sealed are the Eight-Tails and the Nine-Tailed Demon Fox.
Main article: Jinchūriki
Known Tailed Beasts
Main article: One-Tailed Shukaku
It has been captured by Deidara then sealed by the Akatsuki.
Two-Tailed Demon Cat
Main article: Two-Tailed Demon Cat
Three-Tailed Demon Turtle
Main article: Three-Tailed Demon Turtle
Main article: Four-Tailed Beast
It has been captured by Kisame then sealed by the Akatsuki.
The Five-Tails (五尾, Gobi) is a demon sealed within an unnamed shinobi from Iwagakure. It has been captured and sealed by the Akatsuki.
The Six-Tails (六尾, Rokubi) is a demon sealed within an unnamed young man of unknown origins. It has been captured and sealed by the Akatsuki.
Eight-Tailed Demon Ox
Main article: Eight-Tailed Beast
Nine-Tailed Demon Fox
Main article: Nine-Tailed Demon Fox
Legend of the Tailed Beasts
According to some fans, the "Legend of the Tailed Beasts" is an epic story from Japanese folklore which Naruto author Masashi Kishimoto draws from to create the Tailed Beasts in his work. However, it is an example of internet-based fake lore which originated on Chinese websites, some suspect this Chinese site.
The veracity of the legend breaks when it is cross-referenced with non-fandom sources on Japanese folklore. For example, the isonade, which is held to be the Three-Tails in this account, is in fact equipped with only one large, hook-covered tail; and the hōkō which is actually a Chinese creature called a pénghoú, named as the Five-Tails, has no tail at all. The badger was said to be the lord of all the Tailed Beasts in the original legend, and Naruto fans have claimed that a certain Tailed Beast to be a badger instead of it's true form, which was a tanuki for the One-Tailed Shukaku.
Additionally the author of the story admitted it was not a true legend, unfortunately it has gone largely unnoticed by most fans of the story.