Moon

The is a planetary body orbiting the world. The moon was used by the first jinchūriki, the Sage of the Six Paths, through his fūinjutsu The Sage   seal the physical remains of the Ten-Tails after he used his Creation of All Things ability to divide its chakra into the nine tailed beasts. Madara Uchiha, after awakening the Rinnegan, released the seal placed on the empty vessel of the Ten-Tails and summoned it back to earth.

Madara's ultimate plan, that was later adopted by Obito Uchiha, the Eye of the Moon Plan, involved reviving the Ten-Tails through joining the other tailed beasts, becoming its jinchūriki, and then projecting his eyes onto the moon in order to cast his "Infinite Tsukuyomi": a perpetual, world-scale genjutsu cast on every living being on the planet, which will allow both Madara and Obito to control and unite them to create a world with neither war nor hatred, making themselves the rulers of the world but at the cost of eliminating free will from humanity.

Later, after the revival and subsequent battle with Kaguya Ōtsutsuki, Naruto Uzumaki and Sasuke Uchiha worked together to create a very similar satellite in her core dimension in order to re-seal her.

Trivia

 * Because of the moon's origin and it being the holder of the Ten-Tails' body, tailed beasts and subsequently their jinchūriki are affected by it, and much more so during a full moon.
 * According to Gaara, Shukaku relishes the opportunity to kill anyone in sight at any time because of its innate rage and blood-lust, but especially so during the full moon.
 * In the anime, Fukai, during his time as Gyūki's jinchūriki, noted that he would have trouble sleeping at night, especially during a full moon and at one point was shown to have to suppress a partial manifestation of Gyūki's tail after he had been staring at the full moon. Fukai was also shown to take sleep pills to help with this side-effect of being a jinchūriki.
 * During significant events, the colouring of the moon is usually red.