The Three-Tailed Giant Turtle (三尾の巨大亀, Sanbi no Kyodaigame) is a large, turtle-like tailed beast. It was formerly sealed in Yagura. The Three-Tails receives much more attention in the anime than the manga.
Background
At some point in the past, the Three-Tails was sealed within Yagura from Kirigakure. It was later extracted from its host for some reason and escaped into the wild. Because it did not have a host it was not smart enough to effectively utilize its great strength, instead being reduced to animal instincts.
Three-Tails Arrival arc
In the anime, Orochimaru instructs Kabuto Yakushi and Team Guren to take a young boy named Yūkimaru to a lake. When they arrive, Kabuto forces Yūkimaru to release all of his chakra, causing the Three-Tails to begin to surface from the lake. With Guren's help the beast is completely revealed and they attempt to capture it. Their attempts prove insufficient and the beasts creates a large tidal wave to wash its attackers away.
The tidal wave gains the attention of a group of Konoha ninja, who try to use Four-Corner Sealing Barrier to permanently trap it in its own dimension. Just when the sealing begins to work the Konoha ninja are interrupted by Guren, prompting the beast to attack them all. Yūkimaru is able to calm the beast down temporarily, but when he tires out the Three-Tails turns its attention to him. Guren and Naruto Uzumaki come to his defense and are swallowed in the process. With the help of their allies on the outside they are able to escape and the Konoha ninja try once more to seal the beast.
Just when the sealing is almost complete, Yūkimaru, angered by the apparent death of Guren, empowers the beast to break free of its restraints. The Three-Tails goes on a rampage and attacks everyone nearby, crushing Nurari, Kigiri, and Kiho. Its attempts to attack Yūkimaru, however, have no effect. It is only through the use of the Wind Release: Toad Oil Flame Bullet that the beast is driven away. The sealing attempt is left to ANBU members and the remaining Konoha ninja go home. Deidara and Tobi of Akatsuki soon find these ANBU members and dispose of them.
The beast's capture takes place much earlier in the manga (at the start of the Hidan and Kakuzu arc), but plays out in much the same way as in the anime. Tobi and Deidara confront the beast, to which it responds by chasing Tobi. With the Three-Tails distracted, Deidara molded an explosive clay fish in an attempt to capture it. It's unclear if this marked the end of the battle, as the remainder of the battle goes unseen. As the two towed the Three-Tails to the Akatsuki's lair after the battle, Tobi gloated of bringing the Three-Tails down with his special jutsu, but Deidara thought otherwise. It is later sealed in the sealing statue.
Abilities
Other than being a very fast swimmer given its size, the Three-Tails' abilities are not seen in the manga. Tobi suggests that Kisame would have been a better choice for capturing the beast given its affinity for water. In the anime its abilities are greatly elaborated upon, many of which deal with its size: it can roar to repel attacks; it can produce a large tidal wave that spreads away from it in all directions; it can strike with one of its three spiked tails to break through most defenses. Its skin is, similarly, resistant to attack.
Of the beast's more specialized abilities, it can produce a hallucinogenic mist that exploits the victim's insecurities and forces the victim to face them. It can also shoot white, Menacing Ball-like shockwaves. When it swallows something, thousands of "mini-clones" of itself will attack what it has eaten within its gut, presumably to facilitate in digestion.
Influence
Turtles are often used as the base design for sea monsters in generic Japanese folklore. The Three-Tails' design in particular was conceived as a result of series creator Masashi Kishimoto's interest in monsters, yōkai, and kaijū, mixing together various elements of those types of creatures to create a monster with a turtle's body and a shrimp's tail with a crab-looking figure.