The Infinite Tsukuyomi (無限月読, Mugen Tsukuyomi) is a technique which is the key to Madara's Eye of the Moon Plan.
By establishing eye contact with only a standard Sharingan, the user can create an empty dimension under their control, which can be then filled with contents of his or her desire, using the power of the Shinju to do so. While physically tethered and connected to the Demonic Statue of the Outer Path, Madara can manipulate the otherwise blank and white world to create anything he wants no matter how detailed, and control it. By doing this he can create a world exactly as he wants.
To trap every human being in this genjutsu, however, the Sharingan has to reflect onto the moon's surface using the eye of the Shinju. In order to do this, (with the exception of Kaguya) one must become its jinchūriki while possessing the power of the Rinnegan. Upon getting close to the moon within the sky, the jinchūriki can remove the natural plating from their forehead to manifest a third eye in the form of the Shinju's Sharingan.
The technique can also be done by assimilating a person into the Shinju. Once this is done, the person is locked in a permanent genjutsu yet will live endlessly from the Shinju's power.
In Naruto 6: Road to Ninja, Obito casts a trial version of the Infinite Tsukuyomi, the "Limited Tsukuyomi" (限定月読, Gentei Tsukuyomi), on Naruto and Sakura, which provides the alternate reality setting of the movie. Instead of casting it off of the moon, he instead used a crystal ball to serve as a medium to cast and host the alternate world.