“Kamikakushi” means “hidden by the kami”, and could be translated “Spirited Away”. Indeed, the Japanese title of the Miyazaki anime called “Spirited Away” in English is “Sen to Chihiro no Kamikakushi”: “Sen and Chihiro’s Kamikakushi”. Historically, it was thought that people who entered particular sacred areas, such as forests or mountains, might be taken away by the kami. Very occasionally, they might reappear years later.
The oldest legend clearly referring to this idea is that of Urashima Tarō, a story that is known to have existed since the eighth century at the latest. In this, a young fisherman helps a turtle back to the sea, and, in gratitude, is carried away to a palace, where he spends several days, maybe weeks, enjoying himself, and falling in love with the princess there. However, he misses his family, and is concerned that they might be worried about him, so he asks for permission to go back. The princess is reluctant, but eventually she is persuaded, giving him a small box, but making him promise not to open it. The turtle takes him back, but although he recognises the place, there is no sign of the village, let alone his family. After searching the beach, he finds the remains of his family home. In horror, he opens the box, and all the years he spent away catch up with him in a moment, as he ages, dies, and decays into dust that scatters on the wind from the sea.
It seems that this term was in fairly common use for people who disappeared suddenly, particularly if they reappeared later with no mundane explanation of where they had gone. It seems likely that many cases were people who became lost in the mountains or forests, or ran away from home, or were murdered, or died in an accident. Indeed, it may have been used by people who knew perfectly well what had happened, just as a polite term to avoid upsetting the people left behind too much. Many of the customs for getting people back from kamikakushi seem to have involved banging drums or otherwise making a lot of noise, while calling out their names and marching around the area: obviously, if someone was lost in the forests fairly close to their village, this would be extremely effective. On the other hand, there have been cases where someone has claimed to have been taken by the kami, in a supernatural sense, and to have come back, and scholars have investigated their stories. However, these cases seem to always have been rare, and I have not come across any recent ones. It does seem that there was a genuine belief that, sometimes, the kami (later, often tengu, a particular kind of mountain spirit) took people away for a time or permanently.
This idea makes a great plot element, whether or not the cause is supernatural, and so kamikakushi is quite popular in fiction. On the other hand, it does not appear to be very important in contemporary Shinto practice, nor in contemporary superstitions. I believe there may be some particular places where there are particular superstitions about kamikakushi, but it is not something I have come across as a general belief. The spread of GPS systems and mountain rescue teams may have reduced the incidence of such problems substantially.
The partner concept of “kamikakurë”, which means “hiding kami”, is more common in the myths, and often means that a kami has, in some sense, died — withdrawing from active participation in the world. This idea is very common in the legends, but, again, less common today, possibly because priests are not interested in emphasising the idea that any kami is dead, or avoiding acting in the world. It is hard to see the point in honouring such a kami at a jinja, after all. It is also clear that the “death” of a kami was not taken to be permanent, or particularly disabling, which no doubt explains the use of a different verb. A kami who had hidden themselves might later reappear, just like a person who had been hidden by the kami.