In "Naruto" the tailed beasts are mythical creatures based on demons from Japanese mythology. These demons are characterized by the number of tails that each one has. Ten total beasts are mentioned in the series and each has a distinct number of tails. For example, the main character, Naruto, is possessed by the nine-tailed demon fox. Beasts one through nine have been sealed away in characters throughout the series which endow those characters with special abilities. One of the main stories in the series is the hunt to capture all of the tailed beasts by the ninja group the Akatsuki.
Tailed beasts one through nine are locked away in a specific individual. The tailed beasts are: One-Tailed Shukaku, Two-Tailed Monster Cat, Three-Tailed Giant Turtle, Four-Tailed Monkey, Five-Tailed Dolphin Horse, Six-Tailed Slug, Seven-Tailed Horned Beetle, Eight-Tailed Giant Ox and the Nine-Tailed Demon Fox. The characters who were possessed by the tailed beasts are Gaara, Yugito Nii, Yagura, Roshi, Han, Utakata, Fu, Killer Bee and Naruto respectively. Each of these tailed beasts were created when the Ten-Tailed beast was separated and sealed by the Sage of the Six Paths.
The tailed beasts of "Naruto" are living forms of chakra that take the shape of various animals. During the series the beasts are sealed within humans. The individuals who are infused with the beasts gain the ability to use their large amounts of chakra. The added amount of chakra gives each human a large amount of power which is comparable to many high level ninjas. For example, even as a teenager, Naruto is able to defeat various enemies who were more powerful and experienced. During battle, each individual can become fully charged with the power of their tailed beast. At this point, they will begin to take the shape of said creature and have full access to their power.
The tailed beasts play a central role throughout the "Naruto" series. In the beginning, Naruto is despised and feared by many of the villagers because they know he is possessed by the beast. As he grows older, he learns how to better control the nine-tailed fox's power and begins to use it to protect the Hidden Leaf village. During the "Naruto: Shippuden" series, the tailed beasts are hunted by the ninja group, the Akatsuki. They are looking to capture all of the tailed beasts because their leader, Madara Uchiha, wants to rejoin them into the ten-tailed beast and use its power to place the whole world under his control.