Kamui

Kakashi's original dōjutsu, released from the Mangekyō Sharingan, that allows one to transfer anything to another dimension. If one spends a lot of time and trains one's chakra over and over again, this technique can be invoked. The target is enveloped with a barrier space and the user concentrates their mind to what they gaze at. The target can struggle helplessly, but against this technique no defence is possible. When the technique is invoked, the space at the centre of the barrier is distorted and the target inside the barrier is drawn in completely. The location and size of the barrier can be specified at will. It is a dreadful technique that, with skilled use and enough chakra, can even pull an entire human being into another dimension.

The Mangekyō Sharingan is a dōjutsu that, with continuous usage, burdens the user with the loss of their eyesight. Since this is the source of Kamui, using it in rapid succession puts Kakashi's body at risk as well. As his Sharingan was transplanted, usage of this technique poses an even greater risk to Kakashi.

Kakashi is able to use this technique up to at least three times in a given day, even when starting at full strength. At first Kakashi's aim and control over the size of the barrier was imperfect. Over time his aim and control improved, as he was able to accurately warp away small and fast moving objects, such as a nail. Kakashi is even able to consecutively warp away two fast-moving arrows.

During the Fourth Shinobi World War, Kakashi learned there is a connection between his technique and Tobi's Space–Time Migration as both acquired their Sharingan from Obito Uchiha and thus share access to the dimension through their respective techniques. Learning of the connection yet unaware of its nature in relation to his friend, Kakashi teleport objects into the other dimension to hit whatever part of Tobi exists there to counter his intangibility.

Influence
Kamui is the word for a divine being in Ainu mythology, although it is almost never written with kanji in modern times. In a more general Japanese context, Kamui refers to the might and majesty of the gods, particularly the Shintō Kami.

Trivia

 * When Kakashi attempted to use this technique on Tobi, he told him not to bother trying as it would be useless. This would hint that Tobi knew where he would end up and simply escape it.
 * The Third Databook seems to hint that other Mangekyō Sharingan users can access the technique, though this is unconfirmed.